These three terms get used interchangeably in everyday conversation, but they are legally and practically different documents, sent at different points in a job.
Quote (or estimate)
Sent before the work starts. A quote states what you will charge for a defined scope of work, so the customer can decide whether to go ahead. A quote is not a request for payment, and (depending on how you word it) may or may not be a binding commitment to that exact price.
Invoice
Sent after the work is done (or at agreed milestones during a longer job). An invoice is a formal request for payment for goods or services already provided, with a due date and, in the UK, specific required details (see our sole trader invoicing guide).
Receipt
Sent after payment is received. A receipt confirms that a specific amount was paid, on a specific date, for a specific invoice. It is proof of payment, not a request for it - the opposite direction from an invoice.
Why the distinction matters
Sending an invoice when you meant to send a quote can make a client think they already owe money for work they haven't approved yet - a fast way to damage trust with a new client. Keeping the three clearly separate, and labelled as what they are, avoids that entirely.