When you cancel or change a patient's subscription, you'll be given an option of whether to pro-rate the change.
If you pro-rate the change that the system will stop the old subscription, refund them the remainder of the term and then charge a pro-rated amount for the remainder of the month. For instance, if you change a patient from a $50/month subscription to a $75/month subscription then the system will refund roughly $25 (refunding the remaining time on the lower-cost subscription) and it will the change them roughly $37.50 to pay for remaining two weeks under the new, more expensive plan.
If you chose not to prorate, then the original payment will be left alone and the new subscription (if you're not cancelling) will start effective the next date of payment.
Note: When Stripe refunds/charges prorated plans it uses an internal logic to set the order-of-operations to reduce the likelihood of a transaction being declined. Sometimes it will issue a refund immediately, then charge for the difference, sometimes it will leave everything alone until the next billing cycle and then charge a non-standard amount that takes into account any pro-rated balances, and sometimes it will do some of both. The amount of money ultimately collected will be the same, but it can sometimes be confusing when looking at your statement.