Typically: An "invoice" is a formal name for what's commonly called a "bill." A business sends you an invoice that says you owe them money. An invoice will typically say how quickly you are supposed to pay it: "due June 30th" or "terms net 30 days." A "receipt" acknowledges that you've paid something. It is signed by the business that receives your money. The business acknowledges "receipt" of your money. You can use it later to prove you paid. Sometimes a receipt is a separate piece of paper. However, a business can also take the invoice and use a rubber stamp on it that says "paid." This is called a "receipted bill." For example: you get a bill from the electric company saying you owe $67.89 for May. The bill says "invoice" on it. Their offices are nearby, so instead of mailing a check, you decide to save the cost of postage by paying in person. You go to the office and give them cash over the counter. They give you a receipt. Next month you get an overdue payment notice. You telephone them. They say "We don't have any record that you paid our May invoice." You say "There must be some mistake, I have the receipt." You can also get a "receipt" for things other than money. The police might say "Sorry, sir, we have to take these but we'll give you a receipt for them and you can claim them at precinct office." It is a VERY UNUSUAL use but "receipt" CAN also mean a cooking recipe. "These brownies are delicious." "Thank you, I made them from my mother's receipt."

An invoice is a bill, a request for payment which has not been made. A receipt is a documentation of payment that has already been made.