「schedule」と「appointment」の違い

Recently someone told me:

× Sorry, I can't meet you at that time because I have a schedule.
○ Sorry, I can't meet you at that time because I have another appointment.
○ Sorry, I can't meet you at that time because I have something on my schedule at that time.

Everyone has a schedule. Your schedule is your list of appointments and free time. You might have two schedules: your work schedule, and your private schedule. You can talk about your Monday schedule, meaning the set of appointments you have on Monday.

When you have to meet someone, that is an appointment. When you are seeing a doctor, that is an appointment. Both of these appointments are on your schedule.

Back in March, I visited America. I had a busy schedule. One of the appointments I had in New York City was to meet some people at a restaurant I used to frequently go to. The restaurant is called Veselka, and it serves Ukrainian food like these pierogis. Two of them were cheese pierogis, and the other two were potato, if my memory is correct. There's also a stuffed cabbage on this plate with mushroom gravy. It's a great restaurant, and you should eat there if you visit New York.