Orders and invoices differ, in that an invoice has a financial record associated with it and is recorded in Accounts Receivable (AR). Orders do not have associated financial records.
An order is created when a customer makes a purchase and wants to be billed instead of paying for the item at the time of the order ("bill me" is selected during check-out). An order does not have a financial record associated with it.
An invoice for a purchase is created when payment is made or expected, likely because the customer has actually ordered an item and already agreed to pay at the time of the order (rather than selecting "bill me" and creating an open order as described above). An invoice also has payment terms. For example, terms of payment might be to pay immediately, pay upon receipt, or pay within 30 days. The invoice has a financial record associated with it and is recorded in Accounts Receivable (AR).
An order is converted into an invoice when:
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the Create Invoice option is selected during the Shopping Cart check-out process.
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the Invoice Me link on the Order Profile is clicked.
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partial or full payment is made for the order.
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the order is prepared for shipping (order fulfillment).