Your Clients calendar does not let two appointments take the same hour, even when you are creating them at the same time from two different places.

When you confirm an appointment, that slot is held in that person's name while the save finishes, and then becomes taken. If someone tries to confirm another appointment for the same hour in that moment, the second one is not saved and you get a notice that the slot has just been taken. The same goes for the blocks you create yourself (see «Setting your availability and blocking time by hand»): they take the hour exactly as an appointment does.

This protection covers what happens inside your calendar. The date preferences arriving from one of your pages' forms do not reserve anything yet (see «A customer's journey: from ad to appointment»), so two people can indeed ask you for the same hour: when you confirm the first, the second stops being available and you will have to offer them another.