curl up vs bend

curl up is not a noun while bend is a noun.

Word	Noun	Adjective	Verb	Adverb
curl up	No	No	Yes	No
bend	Yes	No	Yes	No

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

Other hypernyms of curl up include flex.

curl up (noun)	bend (noun)
	curved segment (of a road or river or railroad track etc.)
	diagonal line traversing a shield from the upper right corner to the lower left
	movement that causes the formation of a curve
	an angular or rounded shape made by folding
	a circular segment of a curve

curl up (verb)	bend (verb)
shape one's body into a curl	cause (an object) to assume a crooked or angular form
	bend a joint
	form a curve
	change direction
	turn from a straight course, fixed direction, or line of interest
	bend one's back forward from the waist on down