That sounds like a sitdown machine (set into a table) rather than a long arm...not quite your domestic machine, but also not a long arm on a frame. Unfortunately since the sitdowns came out, many contests don't know which category to put them in.
The main difference is that in domestic and sitdowns - "home machines", the quilter is using the same process of moving the fabric rather than the machine. In Long-arm machines, the fabric is still and the machine is moving.
I suspect that is where "home machine" came into play...the fact that you move the fabric rather than the machine.