fold up vs tuck

fold up is not a noun while tuck is a noun.

Word	Noun	Adjective	Verb	Adverb
fold up	No	No	Yes	No
tuck	Yes	No	Yes	No

As verbs, tuck is a hyponym of fold up; that is, tuck is a word with a more specific, narrower meaning than fold up:

fold up (noun)	tuck (noun)
	a narrow flattened pleat or fold that is stitched in place
	a straight sword with a narrow blade and two edges
	(sports) a bodily position adopted in some sports (such as diving or skiing) in which the knees are bent and the thighs are drawn close to the chest
	eatables (especially sweets)

fold up (verb)	tuck (verb)
become folded or folded up	fit snugly into
bend or lay so that one part covers the other	make a tuck or several folds in
	draw together into folds or puckers