walk vs cut through

walk is a noun but cut through is not a noun.

Word	Noun	Adjective	Verb	Adverb
walk	Yes	No	Yes	No
cut through	No	No	Yes	No

As verbs, cut through is a hypernym of walk; that is, cut through is a word with a broader meaning than walk:

Other hypernyms of walk include cover, cross, cut across, get across, get over, pass over, track, traverse.

walk (noun)	cut through (noun)
the act of traveling by foot
(baseball) an advance to first base by a batter who receives four balls
a slow gait of a horse in which two feet are always on the ground
the act of walking somewhere
careers in general
a path set aside for walking
manner of walking

walk (verb)	cut through (verb)
obtain a base on balls	travel across or pass over
give a base on balls to
use one's feet to advance; advance by steps
accompany or escort
walk at a pace
traverse or cover by walking
take a walk; go for a walk; walk for pleasure
make walk
live or behave in a specified manner
be or act in association with