Any of the Long Arm type quilting machines have a hopping foot. A Domestic sewing machine uses a foot for free motion quilting that attaches over the needle bar and it normally goes up and down as the needle goes up and down. This is because it must release off the fabric when the needle goes up, so you can move the fabric. There are some free motion feet for domestic machines that don't go up and down, they glide over the surface. Since they glide, they don't actually hold the fabric down when the needle goes down. So you pay a small price in stability. I only really know about Janome machines as far as domestic machines, I have both kinds of free motion feet for that machine- both the "hopping" one and the gliding one. They are about the same really, sometimes I prefer one over the other.
I also have a sweet sixteen sit down, the hopping foot is something I've gotten used to. There is no up and down presser foot like on a domestic machine, so the foot has to go down when the needle goes down to keep the fabric from moving during the time it's going through the fabric. Then it moves upward to allow the fabric to be moved. I hope that makes sense
Kathy