A “statement” is simply the status of the customer’s account at a particular point in time.
Each line item on a statement represents sales transactions, credits, and payments for a given period of time. As such, it doesn’t offer as much detail as the individual sales transactions.
Statements are often sent out on a regular basis (e.g., monthly – let your customers know where they stand and if they still owe you any money).
“Invoice” is a term used by vendors when they want to collect funds from their customers.
When you are creating transactions to receive money from your customers you would refer to it as an Invoice or Sales Receipt.
Invoices are the individual sales transactions that would partially comprise a statement of a customer’s account activity.
Invoices are sent to customers who are not paying immediately when specific work items or goods/services sold are completed or fulfilled (when you are expecting a payment at a later date from a customer). Receive Payment would be used in conjunction with Invoice at the time the customer payment is received.
Sales Receipts are generally used for goods/services rendered at the time of a purchase (sometimes referred to as a “point of sale” purchase), or if customers give you immediate payment.
“Bill” is a term used to describe transactions that are owed to vendors.
When your vendors send you an invoice to collect money from you, it is referred to as a Bill.
Since you are a customer to the vendor, you will receive an invoice from them and enter it as a bill you are expected to pay.