tuck vs fold up

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

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

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

Other hypernyms of tuck include fold, turn up.

tuck (noun)	fold up (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)

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