An appointment is used in a work context, where at least one party is a professional. For example, you might have an appointment at 3pm on Friday to see your doctor, dentist, lawyer or hairdresser. Appointments are always at a specific time, and are marked in a diary or appointment book. Appointments are similar to consultations.
A fixed arrangement is anything that two parties have agreed on. You might have a fixed arrangement to play tennis with your friend tomorrow morning. You might have booked a tennis court or you might not have done. But if both of you have agreed to do this, it can count as a fixed arrangement. This an arrangement, not an appointment.
I hope that makes sense.