An
aid is someone who helps (in various ways), whereas an
aide denotes either of two more specific functions: (1) short for
aide-de-camp, a high-ranking officer in the armed services
(Brigadier Monson summoned his five closest aides for a working lunch—N. Barber, 1984)
, (2) a person employed as an assistant or ancillary worker, especially in a hospital or as a visitor to the home of an ill or elderly person
(Just before he died a nurse's aide brought his dinner tray into the room—E. L. Doctorow, 1989).