Mat Pilates is a type of exercise that involves performing Pilates movements on a mat without the use of a reformer machine. It's based on Joseph Pilates's original Contrology. 

Stretch Pilates" refers to a type of Pilates class that focuses primarily on stretching and improving flexibility, often incorporating longer holds in stretches while still utilizing Pilates principles of controlled movement and deep core engagement, rather than solely building muscle strength like some traditional Pilates classes might do

Reformer Pilates is a full-body, low-impact exercise that uses a specialized machine to improve strength, flexibility, balance, and coordination. The Reformer is a piece of equipment with a moving carriage and adjustable springs that provide resistance. Exercises can be made more challenging or easier.  

Breathing is a key principle in Pilates, and the correct breathing technique can help activate the proper muscles, improve focus, and support the spine. Breathing in Pilates is also known as lateral breathing. It helps activate your abdominals without using your neck or shoulder muscles