hanging vs death penalty

hanging and death penalty both are nouns.

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

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

hanging: a form of capital punishment; victim is suspended by the neck from a gallows or gibbet until dead
death penalty: putting a condemned person to death

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

hanging (noun)	death penalty (noun)
the act of suspending something (hanging it from above so it moves freely)	putting a condemned person to death
a form of capital punishment; victim is suspended by the neck from a gallows or gibbet until dead
decoration that is hung (as a tapestry) on a wall or over a window