When Stripe is connected and ready, an issued invoice's email and Client Portal page have a Pay online button. The customer sees the invoice and its balance and pays it by card through Stripe, without a Magpie account. The payment goes to your Stripe account and is recorded on the invoice automatically, as are refunds made in Stripe. Magpie takes no fee; Stripe's processing fee applies.
Card payments in Invoicing settings turns this on or off, and the invoice page shows the payment link so it can be sent another way. In the mobile app, Share payment link is in the invoice's action menu.