coffee mug vs mug

coffee mug and mug both are nouns.

Word	Noun	Adjective	Verb	Adverb
coffee mug	Yes	No	No	No
mug	Yes	No	Yes	No

As nouns, mug is a hypernym of coffee mug; that is, mug is a word with a broader meaning than coffee mug:

coffee mug (noun)	mug (noun)
a mug intended for serving coffee	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

coffee mug (verb)	mug (verb)
	To stare awkwardly
	rob at gunpoint or with the threat of violence