private vs common soldier

private and common soldier both are nouns.

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

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

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

Other synonyms of private include buck private.

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