stein vs beer mug

stein and beer mug both are nouns.

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

As nouns, stein and beer mug are synonyms defined as:

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