An offer or proposal puts something before one for acceptance or rejection, proposal being the more formal word; a proposition sets forth truth (or what is claimed to be truth) in formal statement.

J. C. Fernald, English Synonyms and Antonyms (1914)

Example sentences

offer I am surprised that she refused such a good offer.
proposal A discussion of the proposal seems to be in order.
suggestion The first suggestion proved to be too complicated.
proffer Good sir, we would like to proffer this wonderful item for your consideration.
statement I'm going to ascertain the truth of his statement.
assertion Tom refuted that assertion with a counterexample.

Popularity over time

Word	1850 → 2019	Trend
proposition		falling
offer		rising
proposal		falling
suggestion		falling
proffer		rising
statement		falling

Use in printed books, per decade from 1850 to 2019.

By length

4 letters: plan¹
5 letters: offer², topic²
6 letters: motion², tender², thesis², dictum²
7 letters: advance², theorem², proffer²
8 letters: question², position³, proposal³, doctrine², overture³
9 letters: statement², assertion³
10 letters: suggestion³
11 letters: declaration⁴, affirmation⁴

The small number after each word is its number of syllables (offer² = 2 syllables).

In other languages

Français: proposition
Italiano: proposizione
Deutsch: Vorschlag
Català: proposició