This is such a great question!
I wish I could say The Events Calendar is ideal for both events and appointments, but I don’t think it is at the moment.
We’re really interested in the idea of being able to split events within events–effectively allowing you to create sub-events that could act as appointments within a parent event. Until then, however, the best suggestion I can offer is to create individual events for each appointment time slot within a given day and sell tickets directly for those posts.
I know that’s not ideal since it could possibly clutter a day on the calendar visually, but does this at least help answer your question? Please let me know.
Thanks,
Geoff