nuclear power vs atomic energy

nuclear power and atomic energy both are nouns.

Word	Noun	Adjective	Verb	Adverb
nuclear power	Yes	No	No	No
atomic energy	Yes	No	No	No

As nouns, atomic energy is a hypernym of nuclear power; that is, atomic energy is a word with a broader meaning than nuclear power:

nuclear power: nuclear energy regarded as a source of electricity for the power grid (for civilian use)
atomic energy: the energy released by a nuclear reaction

Other hypernyms of nuclear power include nuclear energy.

nuclear power (noun)	atomic energy (noun)
nuclear energy regarded as a source of electricity for the power grid (for civilian use)	the energy released by a nuclear reaction