build up vs progress

build up is not a noun while progress is a noun.

Word	Noun	Adjective	Verb	Adverb
build up	No	No	Yes	No
progress	Yes	No	Yes	No

As verbs, build up and progress are synonyms defined as:

Other synonyms of build up include build, work up.

build up (noun)	progress (noun)
	the act of moving forward (as toward a goal)
	gradual improvement or growth or development
	a movement forward

build up (verb)	progress (verb)
form or accumulate steadily	develop in a positive way
enlarge, develop, or increase by degrees or in stages	form or accumulate steadily
change the use of and make available or usable	move forward, also in the metaphorical sense
bolster or strengthen
prepare oneself for a military confrontation