I'm working on an app to book appointments and need to decide what text to use in the button for the last step of the booking process:
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Since we don't have any visual mocks to go by, here's a quick thought on your question; I'll adjust my answer if it's off the mark, or you provide more details.
Starting an interaction: Add or + Appointment is a fairly standard pattern for creating a new instance of an object (in this case an appointment object).
Ending an interaction: Save or Save appointment is often used at the end of a form or dialog as a commitment by the user for the application to save this as a record.
Grammatically speaking, "appointment" requires a determiner. We've gotten so used to menu items sounding like Zork commands that it seems normal, but we have determiners for a reason: they decrease ambiguity. If you say "add an appointment", that clearly means to create a new appointment. If you say "add this appointment", it clearly means to save the appointment that you just created. There's the further ambiguity as to whether "save" means "put aside to deal with later" or "finish". "Set this appointment" would make it clear that clicking the button will result in the appointment being set.
You absolutely should not use “add appointment” in this case.
Your system obviously has a facility to create new appointments, as that’s how the user got here. So you cannot be surprised if the user interprets “add” to mean “create a new record (and cancel the one you are currently creating)”.
You might think it is clear from the user interface language you’ve established elsewhere. Maybe it is clear, once the user has already learned the system. But the label only matters to someone who isn’t sure what the button does.
“Save,” “finish”, “commit” etc. would all be fine; “add” is objectively a bad choice because it could mean its opposite, depending entirely on which reasonable assumption the user makes about how the system works.
(I have encountered this exact problem on my tax return, where I had to stop and think carefully about what to do because I was reluctant to make a mistake)
You haven't given enough context of if customers will be using this or would it be internal staff. The text would also depend on the UI it is on.
I'd recommend you use "Book Appointment" or "Create Appointment"
Also If you were later considering making changes to your appointment, then you might have to consider using 'save' to save changes made.
If the action is to 'Book Appointment', I would stick to having the exact text that describes the action as the button label.
This article might help you.
However, to answer your question above, I personally believe 'Save Appointment' is better than 'Add Appointment'. Unless the 'Add Appointment' would indicate adding the appointment into a calendar/to-do/reminder feature that are within the application itself.