hyperbola vs conic section

hyperbola and conic section both are nouns.

Word	Noun	Adjective	Verb	Adverb
hyperbola	Yes	No	No	No
conic section	Yes	No	No	No

As nouns, conic section is a hypernym of hyperbola; that is, conic section is a word with a broader meaning than hyperbola:

hyperbola: an open curve formed by a plane that cuts the base of a right circular cone
conic section: (geometry) a curve generated by the intersection of a plane and a circular cone

Other hypernyms of hyperbola include conic.

hyperbola (noun)	conic section (noun)
an open curve formed by a plane that cuts the base of a right circular cone	(geometry) a curve generated by the intersection of a plane and a circular cone