hanging vs capital punishment

hanging and capital punishment both are nouns.

Word	Noun	Adjective	Verb	Adverb
hanging	Yes	No	No	No
capital punishment	Yes	No	No	No

As nouns, capital punishment is a hypernym of hanging; that is, capital punishment 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
capital punishment: putting a condemned person to death

Other hypernyms of hanging include death penalty, executing, execution.

hanging (noun)	capital punishment (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