The Simply 16 is the basic machine that many people buy to longarm without any of the fancy features. It is popular for quilters who use computer guided appliances like the PC Quilter or Q-bot. You don't need a machine that has all the bells & whistles if a computer is controlling it. I believe the sit-down model of Handiquilter is probably a Simply 16 with the wheels removed and it has been modified to be controlled with a foot pedal instead of the off/on and speed sliders. I can't get the link for the Sweet 16 to open right now but I think that is the difference. I know the Simply 16 is the basic version for use on a frame. The sit-down Sweet 16 is a new animal that I am not familiar with.
So in short--no, the conversion kit appears to turn a basic Simply 16 into the stitch regulated and hand controlled version--both are for use on a frame.