punning vs fun

punning and fun both are nouns.

Word	Noun	Adjective	Verb	Adverb
punning	Yes	No	No	No
fun	Yes	No	No	No

As nouns, fun is a hypernym of punning; that is, fun is a word with a broader meaning than punning:

punning: a humorous play on words
fun: verbal wit or mockery (often at another's expense but not to be taken seriously)

Other hypernyms of punning include play, sport.

punning (noun)	fun (noun)
a humorous play on words	activities that are enjoyable or amusing
	violent and excited activity
	a disposition to find (or make) causes for amusement
	verbal wit or mockery (often at another's expense but not to be taken seriously)