hold up vs brace

hold up is not a noun while brace is a noun.

Word	Noun	Adjective	Verb	Adverb
hold up	No	No	Yes	No
brace	Yes	No	Yes	No

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

Other hyponyms of hold up include scaffold, block, carry, chock, buoy, buoy up, pole, bracket, underpin, prop, prop up, shore, shore up, truss.

hold up (noun)	brace (noun)
	a structural member used to stiffen a framework
	a carpenter's tool having a crank handle for turning and a socket to hold a bit for boring
	an appliance that corrects dental irregularities
	a support that steadies or strengthens something else
	elastic straps that hold trousers up
	a rope on a square-rigged ship that is used to swing a yard about and secure it
	either of two punctuation marks ({ or }) used to enclose textual material
	a set of two similar things considered as a unit
	two items of the same kind

hold up (verb)	brace (verb)
cause to be slowed down or delayed	cause to be alert and energetic
be the physical support of; carry the weight of	support by bracing
hold up something as an example; hold up one's achievements for admiration	support or hold steady and make steadfast, with or as if with a brace
rob at gunpoint or by means of some other threat	prepare (oneself), often but not necessarily for something unpleasant or difficult
continue to live and avoid dying
resist or withstand wear, criticism, etc.
resist or confront with resistance