conic section vs plane figure

conic section and plane figure both are nouns.

Word	Noun	Adjective	Verb	Adverb
conic section	Yes	No	No	No
plane figure	Yes	No	No	No

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

conic section: (geometry) a curve generated by the intersection of a plane and a circular cone
plane figure: a two-dimensional shape

Other hypernyms of conic section include two-dimensional figure.

conic section (noun)	plane figure (noun)
(geometry) a curve generated by the intersection of a plane and a circular cone	a two-dimensional shape