mug vs drinking vessel

mug and drinking vessel both are nouns.

Word	Noun	Adjective	Verb	Adverb
mug	Yes	No	Yes	No
drinking vessel	Yes	No	No	No

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

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