pooch out vs purse

pooch out is not a noun while purse is a noun.

Word	Noun	Adjective	Verb	Adverb
pooch out	No	No	Yes	No
purse	Yes	No	Yes	No

As verbs, purse is a hypernym of pooch out; that is, purse is a word with a broader meaning than pooch out:

pooch out (noun)	purse (noun)
	a container used for carrying money and small personal items or accessories (especially by women)
	a small bag for carrying money
	a sum of money offered as a prize
	a sum of money spoken of as the contents of a money purse

pooch out (verb)	purse (verb)
round one's lips as if intending to kiss	contract one's lips into a rounded shape
	gather or contract into wrinkles or folds; pucker