Most guides to cryptics offhandedly say that the definition part of a cryptic clue is a synonym for its solution. That's the right level of detail for a quick introduction, but actually there are several established ways of getting from the definition to the solution, most of which definitely aren't strict synonyms. This is an attempt to list these different categories, mainly as a bit of fun, but maybe others will find it interesting too. It's probably all fairly obvious/intuitive for seasoned solvers, and as a result I'm certainly not proposing that everyone learns the jargon below.
It's worth saying that the following also applies to words in the clue being swapped out for other words as part of the wordplay, e.g. "kitty" becoming the letters CAT (one bit of jargon I am trying to introduce is "tokens" as a name for words in the clue which become something else in the wordplay).
In the most familiar type of definition, the definition is just another word for the solution, as in “large” defining BIG. Two words are synonyms if you can construct a sentence where either the definition or the solution could occupy the same slot in the sentence without affecting the sentence's grammar or meaning. If “The house is big” survives translation to “The house is large”, then “large” can define "big" and vice versa.
There are two special cases I'd also classify as synonyms. Firstly, a setter might use an abbreviation or symbol to define a word, e.g. “He” may cunningly define HELIUM or “XL” might define FORTY. Secondly, a setter may use an exclamation or phrase to define something which expresses the same emotion or idea. “Blimey!” could define another way of expressing shock like OH MY GOD or WELL I NEVER, and “that’s disgusting” could define another way of expressing disgust like YUCK or UGH.The simple test: The definition and solution are synonyms if a sentence containing <definition> still means the same thing if you replace it with <solution>.
People often disagree over whether two words are synonyms, but since setters can't go door-to-door asking every potential solver if they agree two words are synonyms, the next best thing is to consult a dictionary or thesaurus - if a synonym is backed up there, it should be familiar to a significant number of people.
It’s also worth remembering that two words which aren’t synonymous in one context might be synonymous in another (“big” might define “tall” even though a big lunch is probably not a tall lunch). Occasionally people forget this and decide that a particular technical usage cancels out other usages (“set” and “group” have specialised meanings in maths, but that doesn’t mean they're not synonyms in everyday life).
It’s also extremely common for the definition to be a term whose meaning is broader than that of the solution, as in “film” defining ROMCOM. Instead of travelling horizontally along a chain of synonyms, we move down a hierarchy of meanings, from broader to more specific terms. I'd suggest calling these definitions by category. Most of these involve common nouns, i.e. nouns which refer to particular types of thing. A broader category can define a narrower subcategory, or - most narrowly of all - a specific individual or member of that category, so “musician” can define subcategories like SINGER or BASSIST, or an individual instance like PAUL MCCARTNEY.
My term "definition by category" perhaps doesn't fit verbs, adjectives and adverbs very well, but these can all be defined in this broad-to-specific way too. A broader verb/verb phrase like “move through water” can define a narrower action like SWIM or WADE, a broader adjective/adjectival phrase like “grey” can define a narrower quality like SILVERY, and a broader adverb/adverbial phrase like “very quickly” can define a narrower phrase like AS SOON AS POSSIBLE.
Sometimes these definitions use words like “what”, “which”, “that”, “who” and “where”, as in “which cobbler uses", “who educates children”, and “where books are kept”. I'd still classify these as definitions by category – it's just that the pronouns further constrain the category in question ("which" means a thing or category of things, "who" means a person or category of people, "where" means a place or category of places etc).
Sometimes it's hard to say if a setter intended a definition to be read as a synonym or as a definition by category, as in the example of “educator” defining TEACHER. The most familiar meaning of "teacher" is the specific category of people who teach children in a school, which would be a subcategory of educators (alongside lecturers, driving instructors, senseis etc). But "teacher" can also more broadly mean anyone who educates or teaches. "Teacher" is therefore both a synonym of "educator" and a more specific category of "educator". Of course, none of this particularly matters: as long as there's at least one intuitive way to get from the definition to the solution, there's no rule against there being an alternative route too.
Can "Paul" define MCCARTNEY without a definition-by-example indicator? Conventional crossword wisdom says no, because Paul's just one example of a McCartney, but I disagree for several reasons. Let's agree on the following at least:
I'd also argue that if [3] means that "animal" can define any word for a member of the category of animals e.g. CAT or KITTY, then [4] should mean that "Paul" can define any word for any member of the category of Pauls, e.g. the word MCCARTNEY, and that "McCartney" can define any word for any member of the category of McCartneys, e.g. the word PAUL. And we know that any word for a category can define either a word for one of its subcategories or a word for one of its examples, again with no special indicator needed.
If you're still not convinced, I'd ask what we're actually doing when we use a definition like "McCartney, perhaps" to define either BASSIST or PAUL. In both cases we're asking solvers to zoom out and find a category which includes someone called McCartney, but for some reason only one of these categories is allowed to "flip over" and act as a definition by category. The category "musician" can define MCCARTNEY, but the category "Paul" suddenly can't. Make it make sense! Let it be!
The definitions mentioned so far are basically about words being equivalent in meaning (or broader or narrower in meaning). There's a fundamental vagueness to these definitions, because a word may have any number of synonyms or subcategories. But there's a type of definition where words are used to provide a unique description which only fits a single entity, as in "capital of France" for Paris or "author of Emma" for Jane Austen. In such cases the solution will be the name of this uniquely described entity (some entities may be referred to by multiple names, but the enumeration given in the clue will normally clarify which is the relevant one).
Unlike synonyms or categories, these "unique description definitions" point directly at the entity which satisfies a particular description (note that "capital of France" and "author of Emma" would mean the same thing if they started with "the"). Definitions like “smallest planet of the solar system” and "New Zealand's national bird" also work like this by presupposing there's exactly one thing that fits the bill. As with definitions by category, these definitions can have “who”, “what”, “where”, “when” etc tagged onto them: “who wrote Wuthering Heights” means “[the single person] who wrote Wuthering Heights” etc.The simple test: A definition is a unique description definition if it makes sense to say "<solution> is the name of the only individual or entity that matches the description of the <definition>".
I'm not saying that whenever a setter defines a solution with a unique description definition, the solver gets that solution for free. A solver could not solve "capital of Georgia" immediately without knowing which Georgia the setter means, but the key point is that the setter did mean one of these options (either "the capital of the US state Georgia" OR "the capital of the country Georgia"). There might be two ways to read the clue, but each of those possible readings is a unique description pointing to exactly one city.
This is quite different from something like "capital of South Africa". Since South Africa has three capitals, the phrase is not enough to express anything definite or unique which could be paraphrased with the word "the". The most the setter can get across with those words is "a capital of South Africa", which would of course have multiple solutions. Whereas "capital of Georgia" can be read as two different unique description definitions, each with a single solution, "capital of South Africa" can only be read as a definition by category.
These definitions are almost a parallel of the unique description definitions I described above. Whereas unique description definitions lead us to the name of a person, creative work, place etc by reference to some unique property of that individual, these dictionary-style definitions lead us to a word by reference to some fairly unique meaning that this word has. Similarly to how "capital of France" really means "the only thing which is the capital of France", what "mammal with bill" means in practical terms is "the only English word which a dictionary might define as 'mammal with bill'".
The simple test: A definition is a dictionary-style definition if it makes sense to say "the only word you'd be likely to define as <definition> is <solution>".
Essentially all the definitions described so far are isolated nouns, verbs, adjectives or adverbs (or noun phrases, verb phrases etc), but sometimes definitions are complete sentences. In particular I mean declarative sentences which consist of (at least) a noun and a verb. These sentences express factual claims about a solution. An example of a sentence definition would be "She wrote Emma" for AUSTEN.
Note the pronoun "she" in that definition. In my opinion, sentence definitions only work if they include a personal pronoun (or a demonstrative pronoun like “this” or “that”, or a term like “thus”, “so” or “in this manner”). The first reason is that these words allow the sentences to refer to the solution rather than just vaguely relate to it. A pronoun-less sentence like "An author wrote Emma" does not cleanly point to AUSTEN or indeed any other word - the only thing that could be equivalent to this sentence would be another sentence.
The second reason these "pointer words" are important is that they give the solver the crucial information of what kind of word they're looking for (noun, verb, etc). With the other definitions we've looked at, this is always clear ("musician" is a noun, so we'll swap that for another noun), but "She wrote Emma" isn't a noun or a verb etc – it's a full sentence. As such, the "she" is necessary to tell the solver they're looking for a noun, specifically a woman, just as the "this" in "Austen did this" might point to a verb like WROTE, the "this" in "Emma was this" might point to an adjective like RICH and the "thus" in "Austen wrote thus" might point to an adverb like IRONICALLY.
The simple test: A definition is sentence definition if replacing a pronoun or other "pointer word" in the sentence with <solution> produces a factual statement or claim.
Occasionally I see clues where the definition is what I'd call an incomplete sentence definition. An example would be "green and spiky" used as a definition for CACTUS or "breaks the law" used as a definition for CRIMINAL. If these phrases contained some extra words (say, "[something which is] green and spiky" or "[someone who] breaks the law"), they'd be valid sentence definitions accurately defining these solutions. As is, these sentence fragments mislead the solver by pointing them at the wrong grammatical category: CACTUS and CRIMINAL are both nouns, but "green and spiky" would normally suggest the solution is an adjective, and "breaks the law" would suggest a verb. The usual rule that the clue will tell the solver what kind of solution they're looking for has been dropped without warning.
Like most setters and solvers I know, I consider such definitions to be inelegant and unfair, almost on a par with giving the wrong number of letters for the solution. Yes, cryptic clues are supposed to be tricksy, but indicating the correct grammatical category of the solution is such a basic requirement that randomly ignoring it in certain clues is annoyingly inconsistent rather than entertainingly misleading, and feels like the sort of goalpost-changing that I worry puts new solvers off. That said, I was interested to see that Ximenes includes such a definition (the verb phrase "Can make you uncommonly sore with flickering tip" defining the noun RIPOSTE) in his famous guide to fair and consistent cluing...