stick up vs mug

stick up is not a noun while mug is a noun.

Word	Noun	Adjective	Verb	Adverb
stick up	No	No	Yes	No
mug	Yes	No	Yes	No

As verbs, mug is a hyponym of stick up; that is, mug is a word with a more specific, narrower meaning than stick up:

stick up (noun)	mug (noun)
	with handle and usually cylindrical
	the human face (`kisser' and `smiler' and `mug' are informal terms for `face' and `phiz' is British)
	a person who is gullible and easy to take advantage of
	the quantity that can be held in a mug

stick up (verb)	mug (verb)
defend against attack or criticism	To stare awkwardly
rob at gunpoint or by means of some other threat	rob at gunpoint or with the threat of violence