"appointment is usually used when referring to a business or necessary meeting like a dentist or doctor's appointment. "date" is used for leisure meetings such as going for a meal with your boy/girl friend or to the movies with your friends.

There isn't much. It's all a matter of formality and social context. "Appointment" is a formal term, and meeting times with doctors, lawyers, etc. are called "appointments." "Date" is interesting because it is often, but by no means always used to refer to a meeting between two people who may be developing a romantic interest in each other. I

Jesse described it exaclty. "Date" is also used in other contexts like "What is the date today" or "the expiration date on this milk is passed". But "a date" compared to "an appoinment" is excalty as Jessee described.