common soldier vs private

common soldier and private both are nouns.

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

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

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

Other synonyms of common soldier include buck private.

common soldier (noun)	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

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