beer mug vs mug

beer mug and mug both are nouns.

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

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

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

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