fun vs punning

fun and punning both are nouns.

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

As nouns, punning is a hyponym of fun; that is, punning is a word with a more specific, narrower meaning than fun:

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

fun (noun)	punning (noun)
activities that are enjoyable or amusing	a humorous play on words
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)