conic vs cone-shaped

conic is a noun but cone-shaped is not a noun.

Word	Noun	Adjective	Verb	Adverb
conic	Yes	Yes	No	No
cone-shaped	No	Yes	No	No

As adjectives, conic and cone-shaped are synonyms defined as:

Other synonyms of conic include conelike, conical.

conic (noun)	cone-shaped (noun)
(geometry) a curve generated by the intersection of a plane and a circular cone

conic (adjective)	cone-shaped (adjective)
relating to or resembling a cone	relating to or resembling a cone