paddy wagon vs police wagon

paddy wagon and police wagon both are nouns.

Word	Noun	Adjective	Verb	Adverb
paddy wagon	Yes	No	No	No
police wagon	Yes	No	No	No

As nouns, paddy wagon and police wagon are synonyms defined as:

Other synonyms of paddy wagon include black Maria, patrol wagon, police van, wagon.

paddy wagon (noun)	police wagon (noun)
van used by police to transport prisoners	van used by police to transport prisoners