【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.