ginger beer vs beverage

ginger beer and beverage both are nouns.

Word	Noun	Adjective	Verb	Adverb
ginger beer	Yes	No	No	No
beverage	Yes	No	No	No

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

ginger beer: carbonated slightly alcoholic drink flavored with fermented ginger
beverage: any liquid suitable for drinking

Other hypernyms of ginger beer include drink, drinkable, potable.

ginger beer (noun)	beverage (noun)
carbonated slightly alcoholic drink flavored with fermented ginger	any liquid suitable for drinking