prescription medicine vs prescription drug

prescription medicine and prescription drug both are nouns.

Word	Noun	Adjective	Verb	Adverb
prescription medicine	Yes	No	No	No
prescription drug	Yes	No	No	No

As nouns, prescription medicine and prescription drug are synonyms defined as:

prescription medicine and prescription drug: a drug that is available only with written instructions from a doctor or dentist to a pharmacist

Other synonyms of prescription medicine include ethical drug, prescription.

prescription medicine (noun)	prescription drug (noun)
a drug that is available only with written instructions from a doctor or dentist to a pharmacist	a drug that is available only with written instructions from a doctor or dentist to a pharmacist