An invoice is a document used in commerce, particularly in retail. It is made by a person or company who is selling something to a customer (or "buyer"). The invoice is given to the customer as a request for payment. It lists the goods or service provided to the customer, along with the price being charged for each of them.
Once the customer has paid for the goods or services, they may be given a receipt. The receipt is the customer's proof that they have paid for the products. A receipt is not the same thing as an invoice.
From the seller's point of view, an invoice is called the sales invoice. From the buyer's point of view, an invoice is called the purchase invoice.