cut into vs rut

cut into is not a noun while rut is a noun.

Word	Noun	Adjective	Verb	Adverb
cut into	No	No	Yes	No
rut	Yes	No	Yes	No

As verbs, rut is a hyponym of cut into; that is, rut is a word with a more specific, narrower meaning than cut into:

Other hyponyms of cut into include furrow, groove, root, rootle, rout, spade, shovel, trowel, burrow, tunnel.

cut into (noun)	rut (noun)
	a settled and monotonous routine that is hard to escape
	a groove or furrow (especially one in soft earth caused by wheels)
	applies to nonhuman mammals: a state or period of heightened sexual arousal and activity

cut into (verb)	rut (verb)
turn up, loosen, or remove earth	hollow out in the form of a furrow or groove
	be in a state of sexual excitement; of male mammals