Usually, connecting an API to your business means that while making a payment, your client is redirected to the payment gateway website and goes back to yours only when the payment is complete. You cannot change the invoice design or affect any other processes that your client undergoes.
With White Label your client stays on your website, while you can manage all processes and customize the invoice design.
Does the fee amount change with White Label? - https://plisio.net/faq/does-the-fee-amount-change-with-white-label
Why does my business need White Label? - https://plisio.net/faq/why-does-my-business-need-white-label