veteran vs veteran soldier

veteran and veteran soldier both are nouns.

Word	Noun	Adjective	Verb	Adverb
veteran	Yes	Yes	No	No
veteran soldier	Yes	No	No	No

As nouns, veteran and veteran soldier are synonyms defined as:

veteran and veteran soldier: a serviceman who has seen considerable active service

veteran (noun)	veteran soldier (noun)
an experienced person who has been through many battles; someone who has given long service	a serviceman who has seen considerable active service
a person who has served in the armed forces
a serviceman who has seen considerable active service

veteran (adjective)	veteran soldier (adjective)
rendered competent through trial and experience