When you receive payment for the invoices, those will be marked on the Shopify admin page as paid – the same place as your retail data.
For smaller purchases (such as product samples), you can also allow the buyers to pay directly at the checkout without going with the order review. You can also limit how much a customer can order before needing to submit the order review.
For example, if you want to let your wholesale clients pay at checkout for orders under $100, set the maximum order amount to $100. Then, the customer can pay for the order at the checkout when the order is under $100 without the hassle of going through the order review. If their order exceeds $100, though, then the customer will have to submit a draft order for you to review.