prescription drug vs prescription medicine

prescription drug and prescription medicine both are nouns.

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

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

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

Other synonyms of prescription drug include ethical drug, prescription.

prescription drug (noun)	prescription medicine (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