small beer vs frivolity

small beer and frivolity both are nouns.

Word	Noun	Adjective	Verb	Adverb
small beer	Yes	No	No	No
frivolity	Yes	No	No	No

As nouns, frivolity is a hyponym of small beer; that is, frivolity is a word with a more specific, narrower meaning than small beer:

Other hyponyms of small beer include bagatelle, fluff, frippery.

small beer (noun)	frivolity (noun)
something of small importance	acting like a clown or buffoon
	something of little value or significance
	the trait of being frivolous; not serious or sensible