murder conviction vs conviction

murder conviction and conviction both are nouns.

Word	Noun	Adjective	Verb	Adverb
murder conviction	Yes	No	No	No
conviction	Yes	No	No	No

As nouns, conviction is a hypernym of murder conviction; that is, conviction is a word with a broader meaning than murder conviction:

murder conviction: conviction for murder
conviction: (criminal law) a final judgment of guilty in a criminal case and the punishment that is imposed

Other hypernyms of murder conviction include condemnation, judgment of conviction, sentence.

murder conviction (noun)	conviction (noun)
conviction for murder	(criminal law) a final judgment of guilty in a criminal case and the punishment that is imposed
	an unshakable belief in something without need for proof or evidence