The words get used interchangeably and they mean different things, with different consequences if the work turns out harder than expected.
An estimate is an informed prediction. It can change if the job changes.
A quote is a fixed price. Once accepted, you are committed to it, whatever you find.
A bid is a quote submitted in competition, usually against a specification somebody else wrote.
Why the distinction costs money
If you call it a quote and the job turns out to need twice the materials, that is your problem. If you called it an estimate and explained why, it is a conversation.
Most disputes about final price are traceable to a document that said "estimate" being treated as a quote by the customer, or the reverse.
Which to give
Quote anything you can see and scope fully. Customers prefer certainty and will often pay a little more for it.
Estimate anything where the work is genuinely unknown until you open it up — old systems, hidden pipework, anything behind a wall. Say plainly what would change the number.
Time and materials is the third option for genuinely unpredictable work: you charge for what it takes. It is honest and it requires more trust, so it suits established customers rather than new ones.
Making either one stick
Write down what is included and what is not. Most arguments are about scope rather than price.
Put an expiry on it. Material prices move, and a quote accepted five months later at last year's price is a loss.
Get acceptance in writing, even informally.
Price extras before doing them — see change orders, which is where construction margin most often disappears.