A canter (or to canter) is a kind of horse’s gait—a gait is any specific style of walking or running. A canter is faster than a trot (a trot is a fast walk), and slower than a gallop (a gallop is a horse’s run). However, canter is not defined by speed; it is a specific way of coordinating the legs that results in a 3-beat step:
As the rider brought the horse up from a trot to a canter, the rhythm of its steps changed, then changed again as they began galloping.
The horse cantered for a while, then broke into a gallop.
One can say also say that a horse is moving at a canter/trot/gallop. The word canter, by the way, came from Canterbury, England.
A cantor is a kind of religious singer in Jewish temples and Christian churches. Cantor is related to the words chant and incantation, among others. The word is most often used for this Jewish religious official, because it is an essential job in a Jewish temple. It is the Jewish cantor’s job to sing solo many sections of the prayer service; melodies which are written in the Torah (which is 3-4,000 years old), can be quite difficult and require specialized training.
A Christian cantor is the leader and instructor of the church’s choir (singing group):
It requires significant scholarship, piety, and singing skill to be a good cantor.