MP vs military police

MP and military police both are nouns.

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

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

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

MP (noun)	military police (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