Other than completely removing the drive, there is another way of checking which drive you have.

The first is to eject the drive itself, and look at how the DVD Tray is cut. Take a look below to try to match your drive with one of the images

If your DVD Tray does not match any of the above, then you have either a BenQ or Lite-On Drive. Now, because the DVD Trays of the BenQ and Lite-On drives are identical (See Below) You will need to have a look at the wires which are used on the drive. Don't worry, you don't have to open your xbox to check this... All you need to do is pop off your faceplate and look at the wires through the keyhole shaped hole located below the DVD Drive