when people refer to short, mid, or long arm they are speaking about a machine that goes onto a quilting frame and you stand up and quilt the sandwich by moving the machine, that's placed into a carriage, over the quilt sandwich.
you can buy quilting robotics to do the quilting for you on a quilting frame.
some people are able to use their embroidery machine to do the quilting - which is another way of doing the quilting with robotics.
most people do leave their machines on the quilting frame all the time so they typically have one machine just for quilting and another just for piecing.
recently mid and long arm machines are being produced to sit inside a table so that you can sit down and quilt instead of standing at a quilting frame.
its really a matter of personal taste - some people love to sit and quilt and others love to stand and frame quilt.
the best way to determine your taste is to do both and see which fits you best - if you go to large quilt shows you will see many companies there selling quilting set ups.