military policeman vs lawman

military policeman and lawman both are nouns.

Word	Noun	Adjective	Verb	Adverb
military policeman	Yes	No	No	No
lawman	Yes	No	No	No

As nouns, lawman is a hypernym of military policeman; that is, lawman is a word with a broader meaning than military policeman:

military policeman: a member of the military police who polices soldiers and guards prisoners
lawman: an officer of the law

Other hypernyms of military policeman include law officer, peace officer.

military policeman (noun)	lawman (noun)
a member of the military police who polices soldiers and guards prisoners	an officer of the law