Hello Wayne,

Yes, it's correct payplans don't store credit card data on site. In case of Stripe , when user fill their card details on payment page then customer profile is created on stripe to get future payments.

Recurring payment using stripe initiates from payplans itself on cron execution. When recurring payment required, on cron job payplans will send payment request to stripe and collect payment. Recurring payment requests will be sent from payplans end.

Does the site each day send data to stripe or does stripe know to auto process until cancelled?
Payment request will sent only when payment needed, not every day from payplans end. If you cancel subscription the future recurring payment will get stopped and subscription will get expire on expiration date (set by previous payment).
https://stackideas.com/docs/payplans/administrators/payment-gateways/stripe

Let me know if you have any query.