army vs military service

army and military service both are nouns.

Word	Noun	Adjective	Verb	Adverb
army	Yes	No	No	No
military service	Yes	No	No	No

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

army: a permanent organization of the military land forces of a nation or state
military service: a force that is a branch of the armed forces

Other hypernyms of army include armed service, service.

army (noun)	military service (noun)
a permanent organization of the military land forces of a nation or state	land tenure by service in the lord's army
a large number of people united for some specific purpose	a force that is a branch of the armed forces