The difference between orders and invoices involve processing product delivery (orders) and processing payments (invoices)
Orders in your eCommerce store are created for generating the delivery of digital, physical (shipped), and subscription products. When someone purchases a product in your eCommerce shopping cart, the system will generate an order for processing the products itself.
Invoices are generated in conjunction with an order for processing the payment for the order. When a customer purchases from your store, an invoice is generated for payment for that order. The user can then select a payment option during checkout that marks the invoice as paid when payment is processed.
You can create orders and invoices separately if you want. For example, if you want to create a free order for a client without charging him anything, you can do so.
Alternatively, a one-off invoice can be generated without an order associated to it. You can do this to charge a client for payment without any products from the system.