Engagement, appointment, rendezvous, tryst, assignation, date mean a promise or an agreement to be in an agreed place at a specified time, usually for a particular purpose.
Engagement is the general term usable in place of any of the others.
Appointment is applied chiefly to an engagement with a person who because of the exigencies of his office, his profession, or his position in life must keep a calendar and apportion his time carefully among those who wish to consult him professionally or confer with him.
Rendezvous may designate a place agreed upon for the meeting of persons, often a group of persons <the old soldiers made the town hall their rendezvous > but it usually connotes a pledge or covenant (often an implicit one) to meet something or someone that cannot be escaped without violation of one’s honor.
Tryst is chiefly poetic; like rendezvous, it may designate the place of meeting (which, however, is more often termed trysting place) as well as the agreement to meet at a certain place, but the latter is the commoner denotation of tryst.
Assignation usually denotes a lovers’ tryst, but it commonly conveys a suggestion of an illicit love or of a clandestine meeting.
Date is used especially of casual engagements between friends or of an agreed meeting between a young man and young woman.