military mission vs mission

military mission and mission both are nouns.

Word	Noun	Adjective	Verb	Adverb
military mission	Yes	No	No	No
mission	Yes	No	No	No

As nouns, military mission and mission are synonyms defined as:

military mission and mission: an operation that is assigned by a higher headquarters

military mission (noun)	mission (noun)
an operation that is assigned by a higher headquarters	a special assignment that is given to a person or group
	an operation that is assigned by a higher headquarters
	the organized work of a religious missionary
	a group of representatives or delegates
	an organization of missionaries in a foreign land sent to carry on religious work