The biggest difference being that a Celebrant is not a member of the clergy.
While the priest receives formal training to perform ceremonies, a Celebrant participates in seminars
and conferences as dictated by his or her country's Celebrant organization.
A more important difference for your wedding however, is that whereas a priest is bound by the religious
conventions and rites of their faith, a Celebrant can tailor the wedding to your own specifications,
pulling in a number of themes, ceremonies and concepts as you'd like.