beer glass vs drinking glass

beer glass and drinking glass both are nouns.

Word	Noun	Adjective	Verb	Adverb
beer glass	Yes	No	No	No
drinking glass	Yes	No	No	No

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

beer glass: a relatively large glass for serving beer
drinking glass: a container made of glass for holding liquids while drinking

Other hypernyms of beer glass include glass.

beer glass (noun)	drinking glass (noun)
a relatively large glass for serving beer	a container made of glass for holding liquids while drinking