Every successful donation creates a gift in Gifts with the method Card. Donors matches the donor by email; if no contact has that email, it creates a new one in People. The gift appears on the donor's timeline and counts toward their giving totals. The money goes to your charity's own Stripe account and pays out to your bank.
Details
An online gift's donor, amount, date, fund and method are fixed by the payment, so only its note can be edited. The gift shows its Stripe confirmation number. It's then receipted or thanked according to the donor's receipt preference and your Auto-receipt value. A monthly donation creates a recurring plan, and each later charge adds another gift.