A loan agreement is a written agreement between a lender that lends money to a borrower in exchange for repayment plus interest. The borrower will be required to pay back the loan in accordance with a payment schedule (unless there is a balloon payment).
An operating agreement is generally written when an LLC is formed, and it is not filed with any government office (a copy is kept by each member). All members, no matter their ownership interest, are required to sign.
A purchase and sale agreement is a contract including the terms and conditions for selling a property in exchange for a specific price. After it is signed, an earnest money deposit is paid by the buyer and is non-refundable if their contingencies are met.