sedative drug vs drug of abuse

sedative drug and drug of abuse both are nouns.

Word	Noun	Adjective	Verb	Adverb
sedative drug	Yes	No	No	No
drug of abuse	Yes	No	No	No

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

sedative drug: a drug that reduces excitability and calms a person
drug of abuse: a drug that is taken for nonmedicinal reasons (usually for mind-altering effects); drug abuse can lead to physical and mental damage and (with some substances) dependence and addiction

Other hypernyms of sedative drug include street drug, medicament, medication, medicinal drug, medicine.

sedative drug (noun)	drug of abuse (noun)
a drug that reduces excitability and calms a person	a drug that is taken for nonmedicinal reasons (usually for mind-altering effects); drug abuse can lead to physical and mental damage and (with some substances) dependence and addiction