mug vs beer mug

mug and beer mug both are nouns.

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

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

Other hyponyms of mug include stein, coffee mug, toby, toby fillpot jug, toby jug.

mug (noun)	beer mug (noun)
with handle and usually cylindrical	a mug intended for serving beer
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

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