Joseph Pilates developed a system of functional exercises that involved all planes of motion.
When I worked at Parrot Cay, I would teach a group Pilates class 6 days a week. And while many guests did Pilates at home and knew what to expect, many were brand new to Pilates.
My favorites were always the husbands and partners of women who did Pilates regularly. They would come to class on the pretense of it being a "stretch class" and then look around confusedly when they were doing side planks, bridging with leg kicks, planks with leg lifts, and push ups.
I would always remind them that Joseph Pilates created a functional exercise system that would prepare people for whatever they would encounter in life. And life is not lived on your back. We have to walk, take stairs (lunging), kneel, sit down and get up (squats), carry things, push and pull things, and lift things.
All of this is included in pilates. We work all the muscles in the body. We squat, sometimes supine against resistance and sometimes standing. We lunge. We do planks on the mat and moving planks on the reformer. We do jumping jacks, boxing exercises, and full body rowing exercises.
We work on abdominal strength, back strength, neck strength, arm strength, leg strength, and put it together into a full body workout. We never stretch without strengthening; we never strengthen without stretching. Mr. Pilates wanted all of the muscles of the body to work together seamlessly, being able to shorten, lengthen, or hold a position as called for and without a hitch.
A pilates class that does not include just about every position is not a complete class. You should stand, sit, lie down supine and prone, as well spend some time on your side. You should flex, extend, rotate, side bend, and stabilize your spine.
And we do everything with an attention to bio-mechanically correct form - abdominal support, spine support, skeletal alignment, and breathing.
In Pilates, that's just how we roll ;).