I have learned it is called a reformer.
Here is a picture of one just like the one I bought. Same brand, same model. I think the Total Gym is a copycat maybe? I didn't work out today because I am sore. Maybe tonight if not tomorrow morning! I like the way I feel after I work out with this machine. I need to find out if using this machine is enough workout OR if I still need to walk on the treadmill. I don't think this machine is for cardio.