military police vs MP

military police and MP both are nouns.

Word	Noun	Adjective	Verb	Adverb
military police	Yes	No	No	No
MP	Yes	No	No	No

As nouns, military police and MP are synonyms defined as:

military police and MP: a military corps that enforces discipline and guards prisoners

military police (noun)	MP (noun)
a military corps that enforces discipline and guards prisoners	a military corps that enforces discipline and guards prisoners
	a member of the military police who polices soldiers and guards prisoners