private vs buck private

private and buck private both are nouns.

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

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

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

Other synonyms of private include common soldier.

private (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

private (adjective)	buck private (adjective)
confined to particular persons or groups or providing privacy
not expressed
concerning one person exclusively
concerning things deeply private and personal