splinter vs carve up

splinter is a noun but carve up is not a noun.

Word	Noun	Adjective	Verb	Adverb
splinter	Yes	No	Yes	No
carve up	No	No	Yes	No

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

Other hypernyms of splinter include dissever, divide, separate, split, split up.

splinter (noun)	carve up (noun)
a small thin sharp bit of wood or glass or metal

splinter (verb)	carve up (verb)
break up into splinters or slivers	separate into parts or portions
withdraw from an organization or communion
divide into slivers or splinters