Short answer
An estimate is a rough price that can change. A quote is a fixed price for a defined job, valid until a stated date, that the client accepts or declines. An invoice is the bill for agreed work, sent when the work or a stage of it is done, or when a deposit is due, with a due date for payment.
Estimate, quote and invoice get used as if they meant the same thing, and that is where many arguments about price start. A client who thought they had a fixed price gets a bigger bill, or a business that sent a rough number finds the client holding them to it.
Below: what each document is for, when to send which, how they differ from a bid, a proposal and a proforma invoice, and wording you can copy so the client always knows whether a price is fixed or approximate.

