Swiss ball, stability ball, resistance ball
 

Whatever you want to call them, I call it a resistance ball but what kid of exercise is it? If you include weights, is it weight lifting, is it calisthenics? Anyone know??

Well, it depends what sort of exercises you're doing on them!

I'd put most stability ball work under resistance/strength training. That being said, if you are running up and down your hallway rolling it in front of you, it's cardio! The ball is so versatile that it can be used for all kinds of things. My physical therapist had me bouncing on one for 10 minutes and it got my heartrate up, so that was definitely cardio.