Both of these live in the Upcoming orders card on the subscription page. Rescheduling moves an order earlier; processing the payment charges it right now and creates the order.
Open the actions menu next to a date and choose Reschedule. The Reschedule upcoming order dialog shows a Billing date field and a calendar. Pick a day and click Save. The app confirms with Order rescheduled successfully.
The Upcoming orders card lists the next billing dates, one per row, each with its own "..." menu.

You can only bring an order forward. The latest selectable day is the day it is already scheduled for.
The earliest selectable day is tomorrow, and never on or before the previous order in the schedule, so orders cannot cross each other.
Skipped orders and paused subscriptions have no reschedule action.
A subscription that belongs to a Club cannot be rescheduled or charged by hand. The club bills everyone on one shared schedule.
On the first order in the list, the actions menu also offers Process payment. The dialog names the date you are pulling forward and warns that the customer will be charged. Click Process now. Nothing is confirmed at that moment: the app sends the charge and waits for the result. If it goes through you get Charge will be processed in a few minutes. If it does not, you get an error instead: the payment failed, the payment provider is not enabled, or there was not enough inventory.
A Bill contract action appears in the page actions at the top right, but only after a renewal failed on inventory. A declined card never puts it there, so retry that one with Process payment above. Shopify allows the charge only when the billing cycle date is within the next 24 hours or already due, so reschedule the next order sooner first if it refuses.
A Mollie subscription is charged by direct debit on its own schedule, and its own page carries the date controls rather than the cards above. Reschedule moves the next charge to any future day, later or earlier, on an active subscription; the day is snapped to the hour your shop bills at. Skip next charge pushes it one interval further out instead. There is no charge-now button here: SEPA money takes days to settle, so pulling a charge forward by hand would confirm nothing at the moment you pressed it.
Skip an upcoming order when the customer wants it later, not sooner.
Read how subscription billing works, including what happens when a payment fails.
Stuck on any of this? Open the chat in the bottom right corner of the app and we will help you set it up.