Both printers can print on individual transfer sheets as well as on roll paper.
It is best though if they are used for roll-printing, as they operate better and produce more this way.
Model J requires less space and is nearly 20% faster.
It comes with a roll feeder.
Forward feeding takes place manually using a button (when inserting the film into the tray) and automatically during printing. Backwards feeding is controlled manually by a button on the printer.
Model Y comes with a roll feeder that has both automatic and manual feeding options, while feeding is controlled either by the roll feeder directly (manually) or by the film feeding sensors (automatically).