The exercise system that uses a spring-equipped frame called a Reformer is Pilates.
Pilates was developed by Joseph Pilates, who originally called his method Contrology. He created exercises intended to coordinate breathing, posture, concentration, control, and whole-body movement. Some exercises use only a mat, while others use specialized apparatus designed to assist or challenge the body.
The Reformer is the best-known Pilates machine. It has a moving carriage, adjustable springs, straps or ropes, and a footbar. The springs provide resistance and can also help support movement, allowing exercises to be adjusted for different abilities. Joseph Pilates originally called the apparatus the Universal Reformer because he believed it could help reform the body.
Pilates is sometimes confused with barre because both are popular studio workouts, but they have different origins and equipment. Spinning centers on stationary cycling, while calisthenics primarily uses bodyweight movements. Pilates can be practiced on a mat, but mat Pilates and Reformer Pilates are not identical: the apparatus changes the resistance, support, and precision of many exercises.