ellipse vs conic section

ellipse and conic section both are nouns.

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

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

ellipse: a closed plane curve resulting from the intersection of a circular cone and a plane cutting completely through it
conic section: (geometry) a curve generated by the intersection of a plane and a circular cone

Other hypernyms of ellipse include conic.

ellipse (noun)	conic section (noun)
a closed plane curve resulting from the intersection of a circular cone and a plane cutting completely through it	(geometry) a curve generated by the intersection of a plane and a circular cone