erect vs put up

erect is an adjective but put up is not an adjective.

Word	Noun	Adjective	Verb	Adverb
erect	No	Yes	Yes	No
put up	No	No	Yes	No

As verbs, erect and put up are synonyms defined as:

Other synonyms of erect include raise, rear, set up.

erect (adjective)	put up (adjective)
upright in position or posture
of sexual organs; stiff and rigid

erect (verb)	put up (verb)
construct, build, or erect	preserve in a can or tin
cause to rise up	put up with something or somebody unpleasant
	propose as a candidate for some honor
	place so as to be noticed
	construct, build, or erect
	make available for sale at an auction
	provide
	provide someone with accomodation
	mount or put up