common soldier vs buck private

common soldier and buck private both are nouns.

Word	Noun	Adjective	Verb	Adverb
common soldier	Yes	No	No	No
buck private	Yes	No	No	No

As nouns, common soldier and buck private are synonyms defined as:

common soldier and buck private: an enlisted man of the lowest rank in the Army or Marines

Other synonyms of common soldier include private.

common soldier (noun)	buck private (noun)
an enlisted man of the lowest rank in the Army or Marines	an enlisted man of the lowest rank in the Army or Marines