crucifixion vs death penalty

crucifixion and death penalty both are nouns.

Word	Noun	Adjective	Verb	Adverb
crucifixion	Yes	No	No	No
death penalty	Yes	No	No	No

As nouns, death penalty is a hypernym of crucifixion; that is, death penalty is a word with a broader meaning than crucifixion:

crucifixion: the act of executing by a method widespread in the ancient world; the victim's hands and feet are bound or nailed to a cross
death penalty: putting a condemned person to death

Other hypernyms of crucifixion include capital punishment, executing, execution.

crucifixion (noun)	death penalty (noun)
the act of executing by a method widespread in the ancient world; the victim's hands and feet are bound or nailed to a cross	putting a condemned person to death
the infliction of extremely painful punishment or suffering