Edit
Booking Page → Services, choose the service, change it and save. Changes apply to new bookings immediately. Appointments that are already booked keep the price and duration they were booked with.
Take it off your page
Hide a service when you do not want new bookings for it but want to keep its history. Existing appointments are unaffected.
Delete
Delete a service you created by mistake. Prefer hiding for anything with history behind it, so your reports stay complete.
Editing from your page
Clicking a service in the booking page editor opens the same service record. There is one source of truth, whichever screen you start from.