punning vs paragram

punning and paragram both are nouns.

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

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

punning: a humorous play on words
paragram: a pun made by changing the letters of a word, especially the initial letter.

punning (noun)	paragram (noun)
a humorous play on words	a pun made by changing the letters of a word, especially the initial letter.