hairspring vs spiral spring

hairspring and spiral spring both are nouns.

Word	Noun	Adjective	Verb	Adverb
hairspring	Yes	No	No	No
spiral spring	Yes	No	No	No

As nouns, spiral spring is a hypernym of hairspring; that is, spiral spring is a word with a broader meaning than hairspring:

hairspring: a fine spiral spring that regulates the movement of the balance wheel in a timepiece
spiral spring: a spring that is wound like a spiral

hairspring (noun)	spiral spring (noun)
a fine spiral spring that regulates the movement of the balance wheel in a timepiece	a spring that is wound like a spiral