busy bee vs eager beaver

busy bee and eager beaver both are nouns.

Word	Noun	Adjective	Verb	Adverb
busy bee	Yes	No	No	No
eager beaver	Yes	No	No	No

As nouns, busy bee and eager beaver are synonyms defined as:

Other synonyms of busy bee include live wire, sharpie, sharpy.

busy bee (noun)	eager beaver (noun)
an alert and energetic person	an alert and energetic person