Invoice, Bill, Contract, Statement
Contracts, invoices, bills, and statements are all defined differently and each has his own purpose.
When you perform service for a customer you give them either a contract or a bill when the job is finished and you don't give them a statement.
When a job is completed you give the customer the contract, or bill and when the customer pays you later the customer he (or she) will often ask for a statement. At this time, we will send only a copy of the first page of the contract when we are dealing with a 1-time customer and a small job. When we are dealing with a large contract we will send the customer a statement only when the balance due exceeds a few weeks.
Most companies call their bill invoices when they break the jobs down for time and materials. When you deal with a supply house everything you purchase is listed on the invoice and you get a statement at the end of the month that lists every invoice.
Most companies only send statements when a customer has an open account with several jobs and/or contracts and the statement is necessary to itemize each job and to give the customer a running total.
Most bills we get such as gasoline bills, credit cards, and cable television are statements.
So, the answer is 'NO' you give your customer a bill or copy of the contract and not a statement unless you intend to carry the balance and get paid a few weeks, or months later.