cocaine addict vs drug addict

cocaine addict and drug addict both are nouns.

Word	Noun	Adjective	Verb	Adverb
cocaine addict	Yes	No	No	No
drug addict	Yes	No	No	No

As nouns, drug addict is a hypernym of cocaine addict; that is, drug addict is a word with a broader meaning than cocaine addict:

Other hypernyms of cocaine addict include junkie, junky.

cocaine addict (noun)	drug addict (noun)
a person addicted to cocaine	a narcotics addict