fillet vs carve

fillet is a noun but carve is not a noun.

Word	Noun	Adjective	Verb	Adverb
fillet	Yes	No	Yes	No
carve	No	No	Yes	No

As verbs, carve is a hypernym of fillet; that is, carve is a word with a broader meaning than fillet:

Other hypernyms of fillet include cut up.

fillet (noun)	carve (noun)
a narrow headband or strip of ribbon worn as a headband
fastener consisting of a narrow strip of welded metal used to join steel members
lace having a square mesh
a bundle of sensory nerve fibers going to the thalamus
a boneless steak cut from the tenderloin of beef
a longitudinal slice or boned side of a fish

fillet (verb)	carve (verb)
cut into filets	cut to pieces
decorate with a lace of geometric designs	form by carving
	engrave or cut by chipping away at a surface