An invoice is a request for payment for goods or services, usually in the context of a credit account. (I have an account with you; you supply me with goods, and invoice me for them; 30 days later I pay the invoice.) A receipt is an acknowledgement of a payment, usually in a cash transaction (I buy groceries in a shop; the shop-keeper gives me a receipt). Bill is another terms for invoice but we don't call that in AE. Because somehow invoice sounds more formal than bill. Just like when you go to restaurant, after you finish your meal, you asked for bill (invoice) and after you pay the bill, the receipt will be issue.

Invoice is raise for future payment. Bill is raised against payment. It means payments comes as per agreement after raising Invoice. Bills raised for immediately payment. Receipt are raised for anything, these are not related to money transition.

觉得这个太搞了@@ 能用中文的请尽量用中文哈 谢谢谢！