What exactly constitutes a pun? Do the words in the pun have to both be extant, or can one be a nonce/nonsense word? — Over the years, I've heard numerous usages of "puns" where one word in the pun is in fact not an extant word, such as:
Any topic not related to elephants is irrelephant.
However, my understanding of what a pun is has only rarely matched what people do in actual real life, namely in that the sentence has to have multiple, non-metaphorical interpretations† which are nevertheless both gramatically correct and lexically appropriate. In the example above, there is usage a nonce word (irrelephant) which seems to be a blend of elephant and irrelevant used for humorous effect. However, this word would be unusable outside of the pun, e.g. Oxfam is an irrelephant charity would not convey the meaning "Oxfam is a charitable organization which does not focus on issues relevant to elephants".
Contrast the previous example with "true" puns according to the criteria above:
Oh, you didn't like my Bavarian pretzels? — Well, the wurst is yet to come!
In example 1, the contrast in meaning is due to an interpretation of go against the grain as an idiom as opposed to a literal interpretation thereof. Likewise, in example 2, there is a contrast between the semantics of wurst and worst, which nevertheless are homographs: The meanings of the two sentences are completely different but are equally acceptable in the given context.
However, despite me being able to suss out differences between puns using nonce blend words and those using only extant words, I seem to be the only person who makes a distinction between the two: For example, numerous usages of both types can be observed in BuzzFeed's In Defense of Puns video and "blending puns" in fact are used much more frequently than the "true" puns I discussed here. Are these both just called "puns"? — Is there no finer-grained terminology for describing these literary devices?
†According to my understanding, a seemingly innocous expression which can be interpreted entirely differently in a different context is a double entendre, meaning that one difference between a double entendre and a pun is that the former is context-dependent where the latter is not (e.g. Groucho Marx' If I said you had a beautiful body, would you hold it against me?); Is this a correct interpretation, or have I got this wrong as well?
