Long-arm machines are typically on frames (and these can vary in length but generally take up a lot of floor space) where you move the machine over the quilt. A long-arm versus a mid-arm is based on the amount of space between the needle and the back of the machine - the space you have available to work with.
I've seen some set-ups at quilt shows that have a computerized component where you can set up the pattern and walk away from the machine (the Homesteader Machine has the Sidesaddle).
I'm planning to do my quilting on my domestic sewing machine - a Bernina 830. It will be a challenge to maneuver the bulk in the small space, but it can be done. I would love an HQ Sweet Sixteen sometime - mid-arm sized - I like the sit-down version which has you move the quilt under the needle as compared to putting it on a frame and moving it over the quilt.
Cheers, K