How to identify the model/version of a Game Boy cartridge without its sticker

Nintendo has two forms of revision numbers that they use for their cartridge games. The first one is the "-n" identifier on the end of the serial number which means that something physical about the cartridge has changed. In 99% of the cases this is an update to the label.

Back in the mid-90's we saw a lot of "-1" games appear because common games that everyone wanted to buy were being distributed when the ESRB was being instituted. There are many games that have a standard version and a "-1" revision simply because the ESRB rating was slapped on the label.

Nintendo's own Player's Choice logo is another good example of many label updates that required a new revision number because of the addition of the Player's Choice badge.

What you are really interested in is the ROM version of the game that is on the memory chip on the PCB. For quality control Nintendo does mark their games with a ROM ID on the outside of the game. For any cartridge game with a label on the back (NES, SNES or N64) there is an impressed number on the sticker. For games with only a sticker on the front (GB, GBC, GBA) the number is impressed on the game label, with the exception of the DS and 3DS, which also have the revision stamped on the back.

This number represents the facility/manufacturing line that the cartridge was assembled on. If your cartridge has the first version of the original ROM you will only see the 2-digit facility number. However, if a new version of the ROM was released from the developer to manufacturing, then a letter was appended to the end of the facility code.

The first revision will be an "A", the second revision will be a "B", and so on. If you take a look at these identifiers you can determine which version of the ROM is on your cartridges. If both games have no revision code, or if they have the same revision code, choosing which game to keep is up to you.

The ROM version can be a bigger deal than the serial number variation, depending on the nature of the ROM change. Nintendo has been known to adjust the art in some of their games for no apparent reason. Choosing which revision is a matter of preference.

You may be wondering where to find out information about specific cartridge ROM variations. The best place to go for a detailed log of variations to game ROMs is The Cutting Room Floor. (Beware, this is a blackhole for retro-gamer nerds, such as myself!)

To be clear, this site DOES NOT distribute game ROM files but they have thoroughly documented differences between the software variations of many games, old and new, for Nintendo and many other systems.

The only unfortunate aspect of TCRF is that they do not claim which revision ID stamped on the game goes with which revision detailed on their site. Instead, they just say "Japanese Version 1" or "US Version 2" when outlining differences of ROM versions. You may have to read the details on specific revisions to determine which ones may exist on your cartridges but that's never a difficult process.

I found Sega Genesis / Mega Drive 101: A beginners guide on Racketboy a great resource.

Is the Genesis exactly the same as the Mega Drive?

The name is just a trademark issue, it was originally the Mega Drive, but was marketed as Genesis in North America since the name had already been registered.

What's the difference between the 1, 2, and 3 versions?

Model 1 - Only version to include a volume control slide switch for the stereo sound output. Supposedly, this model is the easiest to perform modifications on for regional bypasses, overclocking, LED change and S-Video output.

Model 2 - Smaller, simplified design. Stereo output is included in the A/V outputs and there is no volume control for the sound.

Model 3 - Even smaller, harder to hack, not compatible with Sega CD or 32X.

There's a forum thread discussing which of the three is the best model. There's even more information on the different Mega Drive systems on Wikipedia:

During its lifespan, the Sega Mega Drive quite possibly received more officially licensed variations than any other console. While only one major design revision of the console was created during its lifespan, each region has its own peculiarities and unique items, while other variations were exercises in reducing costs (such as the removal of the little-used 9-pin EXT. port) or expanding the capabilities of the Mega Drive.
_{Variations of the Sega Mega Drive}

The article covers all of these variations.

Can I buy a Genesis, and then buy cartridges either for the Mega Drive or the Genesis?

The games are locked per region, but there's a good point on this:

System modifications such as adding region switches and SCART outputs can be readily accomplished on most model 1 and model 2 hardware.

Coincidentally I was considering buying a Model 2, which is also the one with the most votes on the mentioned forum thread, so I guess this pretty much answers my question.