Is a drywall lift different than a sheetrock lift?

No, a drywall lift and a sheetrock lift are both called panel lifts, and they are both exactly the same machine. The only difference is the type of panel that you are putting on it. A panel lift is used to lift panels of drywall or sheetrock up to a certain height and hold in there so that you can easily screw it in place. This reduces the chance of injury, as you do not have to hoist a heavy sheet of paneling yourself or work at awkward angles to screw the panel in place while trying to hold it steady.