They look similar, but they do opposite jobs. An invoice requests payment; a receipt confirms payment was made.
The invoice
You send an invoice before you've been paid. It states what's owed, the due date and how to pay. It's a request and a record of the amount due.
The receipt
You issue a receipt after payment lands. It proves the transaction is complete and is what a customer keeps for their own records or expense claims.
Which do you need?
If you're asking to be paid, send an invoice. If you're confirming money received, issue a receipt. Many small businesses send an invoice, then mark it paid and share proof once payment arrives. In Invoice Forever you can mark an invoice as paid to keep your records straight, and export everything for your accountant.