What is the difference between "Bid, Tender, Offer, and Proposal" ?

There isn't really much difference, as they are all suggesting that the proejct is still in a early stage of its lifecycle, when the scope, cost and time are still being developed. 

The first two terms "Bid" and "tender" might suggest a competitive stage where other parties are also preparing their bids/tenders, while "Offer" and "Proposal" *might* suggest some form of negotiated agreement rather than competitive.

But in practice, all the above terms are probably mixed up but serve the same purpose.

to me the bid is the price that you are will to pay based on the proposal document provided. A bid is usually a competitive process with many parties hoping to win the project. 

an offer is also the price that a company is willing to pay to perfrom the work this may or may not be competitive.

a tender is bascially the same as a bid. 

there is usually a specific deadline associated with all of these