There's really only one context where "proposition" has a meaning that's similar to "offer." It has to do with making an offer to engage in a certain type of physical activity between consenting adults, so I'll have to choose my words carefully to not trigger the very sensitive automatic content filters here on the community questions forum. Let's just say that when someone makes amorous advances by offering a direct invitation to a potential partner, that can referred to as a "proposition."

A "proposition" is a suggestion. For example, "Bill proposed that we go to a restaurant tonight". Bill hasn't offered anything. An "offer" is given, stated, or made. For example, "Bill offered to take us to a restaurant tonight" means that Bill will pay. The offer is a gift, even before we go to the restaurant.

A proposition is an idea or suggestion you present for consideration. An offer is a specific proposal made with the intention of forming a formal agreement or contract.

Proposition: Suggestion or plan for consideration. More informal or tentative. Example: A business idea or proposal. Offer: A definite proposal with specific terms. Legally binding in many contexts (like contracts). Example: An offer to buy or sell something.