offer vs propose

offer is a noun but propose is not a noun.

Word	Noun	Adjective	Verb	Adverb
offer	Yes	No	Yes	No
propose	No	No	Yes	No

As verbs, propose is a hypernym of offer; that is, propose is a word with a broader meaning than offer:

Other hypernyms of offer include project.

As verbs, offer and propose are synonyms defined as:

Other synonyms of offer include declare oneself, pop the question.

offer (noun)	propose (noun)
a usually brief attempt
something offered (as a proposal or bid)
the verbal act of offering

offer (verb)	propose (verb)
put forward for consideration	present for consideration, examination, criticism, etc.
threaten to do something	propose or intend
ask (someone) to marry you	make a proposal, declare a plan for something
produce or introduce on the stage	ask (someone) to marry you
present for acceptance or rejection	put forward; nominate for appointment to an office or for an honor or position
propose a payment
give something useful or necessary to
make available for sale
offer verbally
make available; provide
agree freely
mount or put up
present as an act of worship