mug vs coffee mug

mug and coffee mug both are nouns.

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

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

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

mug (noun)	coffee mug (noun)
with handle and usually cylindrical	a mug intended for serving coffee
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)	coffee mug (verb)
To stare awkwardly
rob at gunpoint or with the threat of violence