motorcycle policeman vs motorcycle cop

motorcycle policeman and motorcycle cop both are nouns.

Word	Noun	Adjective	Verb	Adverb
motorcycle policeman	Yes	No	No	No
motorcycle cop	Yes	No	No	No

As nouns, motorcycle policeman and motorcycle cop are synonyms defined as:

motorcycle policeman and motorcycle cop: a policeman who rides a motorcycle (and who checks the speeds of motorists)

Other synonyms of motorcycle policeman include speed cop.

motorcycle policeman (noun)	motorcycle cop (noun)
a policeman who rides a motorcycle (and who checks the speeds of motorists)	a policeman who rides a motorcycle (and who checks the speeds of motorists)