To check the type of DVD drive you have, eject your DVD drive and compare the type of tray you have to the ones in the images below to determine the type of drive you have.
If your tray looks like the one below, you will have to take your faceplate off and look at the color of the wires in the hole where it shows you.
If you have a LiteOn, the only way to determine which firmware version you have (74850C, 83850C or 93450C) is to actually take apart your Xbox 360 and look at the sticker on top of the drive. If it's a 83850C drive the only way to determine whether it's a v1 or v2 it to attempt to read the firmware on the drive. You can also use the information on www.360drives.com to help you guess at what kind of drive your Xbox 360 has.
You can use the colour of the wires to help you determine whether you have a Samsung or Hitachi without needing to open the drive tray:
If you have an Xbox 360 Slim, you can determin whether you have a LiteOn 16D4S or Hitachi-LG DLN10N (firmware 0500) by ejecting your drive tray and comparing it to the ones in the image below:
The only way to determing whether you have a LiteOn with firmware 0225 or 9504 is to take the Xbox 360 apart and look at the label on top of the drive. You can also use information from www.360drives.com to guess at the type of drive you have.
Below is even more info to help you determine what type of drive you have in you Slim Xbox 360 console. Credits go to Ubergeek.
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This is not an exact science but it’s a very good guide. If you want to know if the 360 slim you are looking at is a 9504 or 0225 then follow these suggestions.
The image below showed us that the drive should be an Hitachi 0500 - and after purchasing - IT WAS ! 
- 11XXX All 0225
- 104XX Mix of 9504 and 0225. Mostly 0225. High Probability that a 9504 is a mislabeled 0225
- 103XX Mix of 9504 and 0225 - mostly 9504
- 102XX All 9504
- 101XX All 9504
- 104X All 9504
Another method is by the serial number on the label (thanks to kiwi1hu). The 4th Digital on the end can also give an indication as to what the drive is (again not 100% but results have shown a very high probability)
- 2: 9504
- 3: 0225
- 4 or 0: 0500 Hitachi
Hitachi 0500 have been found in very small numbers in lots 1052X, 1048X, 1047X, 1045X, 1044X, 1028X (EU)
The only way to be 100% sure is to hook your drive up to the latest Jungle Flasher and see what the model / firmware version is.
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*The images on this page were not created by me, all credits go to the respective authors.