The rotator cuff in your shoulder is really four tendons that are at the shoulder, helping it move as it should. If one of those tendons is injured, it is called a tear or injury to the rotator cuff. However, there is a difference as to which tendon you injure and how severely you injure it.
Professional ball players may tear a rotator cuff because of the velocity at which they throw the ball. In their case, the velocity is so strong, they could end up developing a deep or extensive tear in more than one tendon. Your injury is caused by a different mechanism, but it is still a rotator cuff injury. Without seeing your records, it would be impossible to tell you if you injured the same tendons that a ball player might or if your injury is as severe.