Use an online payment gateway for the collection part of a sale when your website needs payment capabilities that the accounting product's invoice-payment connection does not provide. That may mean a checkout tied to a shopping cart, payment confirmation linked to fulfillment, or a supported way to manage separate authorization and capture.
This is usually a decision about where to accept payment, not whether to stop using accounting software. Cloud accounting remains useful for invoices, expenses, bank reconciliation, and financial reporting. Often the best arrangement connects a payment service to accounting rather than asking either system to do both jobs alone.