here is how this should go... first your buyer will submit you a proof of funds (hard or soft whichever is acceptable to you) and an LOI (letter of intent to write a contract) The LOI should be followed with an offer if you like the offer then you accept if not you counter or reject. IF you like the offer then you enter escrow or u go to a closing attorney (depends on the state) THEN and ONLY THEN will you property be taken off the market. Make sure you get a deposit so if it falls through your buyer pays a penalty for the lost time.
The letter of Intent is an intent to write a contract. Usually associated with large contracts. Sometimes used by others trying to tie up a property/take it off the market.
If this is in reference to a property...do not sign...you do not want to arbitarily take a property off the market unless there is a substantial monetary hold somewhere to protect from a fall through on the actual sale.
I have never heard the term LOA. I am assuming it is Letter of Acceptance. If I have a customer who is making an offer, we submit the LOI first. We negotiate terms and then it goes straight to contract. If you are doing a Letter of Acceptance, it would come after LOI and negotiations.
Neither is enforceable unless all the material terms of the contract are included (rarely done) and signed by both parties. Even though a LOI comes first, it is irrelevant from a legal perspective. Usually a LOI is subject to approval and signed contract anyway. Binders are also useless as enforcement tools.