[AT&T Samsung Galaxy Note II] Darkshado:
Go easy on the long quotes when you reply, they're not always necessary. ;)

According to good ol' Wikipedia, sixteen. You'll come across two in Canada (I317M/T889V). I'll focus on those, as well as the other Qualcomm baseband, HSPA/LTE variants like the N7105 and U.S. I317/T889.

The BIOS analogy is clunky in my eye. After all, six same-model motherboards would have the same BIOS, eventual subsequent manufacturer updates notwithstanding.

Phone models and by extension their ROMs can be carrier-specific in a few different ways, for both technical and commercial reasons.

AFAIK a lot of modern cellular modems are partially or entirely software defined, thus can and will be optimized for a given region of the world, or a specific network. In addition, a carrier may want to discourage former subscribers from taking its phones elsewhere.

In the LTE Note 2 this takes place at three levels:

The modem image itself: For instance the AT&T I317 modems do not allow the user to select individual bands to run on, allegedly to force users on LTE. This may be more efficient for the network itself, but a pain for the user if LTE coverage is marginal compared to HSPA in a given location (more so if the HSPA is on 850 and the LTE on AWS, the former having better building penetration). The T889V modem has LTE disabled in software, because as of writing this, no T889V provider has an active LTE network.

Different modems may support different bands entirely, see the modem cross-flashing done on the original Note models to change them from 850/1900 to AWS and back.

NV items: The I317/I317M don't have AWS HSPA enabled even though they are perfectly capable of handling it, as is the modem image installed. They already run AWS LTE out of the box, and consider how trivial it is to apply the AWS mod.

CSC settings, which in turn seem to affect certain NV items, and a few non-NV item network related settings: e.g. APN settings. The CSC settings (probably something like "carrier-specific content") are applied after a factory reset. Among network-related settings controlled by CSC: APN settings and whether they can be edited, HD Voice, fast dormancy. Which network a phone should lock itself to initially also seems to be determined by the applied CSC. On the Note 2, I haven't tested if dialing the code to change it would change the lock or relock the phone. It's on here somewhere; caution, as it does factory reset the phone without warning. Back when I had a Galaxy Gio as a backup, the original CSC files had the nasty habit of relocking the phone if you factory reset it without a "foreign" SIM in it.

Then you've got the user interface plus carrier branded content and apps. These modifications can be done in two locations:

CSC settings: the CSC folders also contain any wallpapers, ringtones, and apps your carrier wants you to have. (Such as Rogers' One Number or Bell TV) Many deem this "bloatware" and want to get rid of it. Back in the Gingerbread days, you needed root to remove those, whereas with ICS and up you can at least hide the apps from the launcher's menu. Some ROMs (I think the US Note 2 ROMs are like this) only have one CSC built-in. Canadian and international ROMs are multi-carrier.

The ROM itself: IMO, AT&T and T-Mobile are more likely to do this than Robellus, as it really makes a ROM single-carrier. It may be preferable for features requiring deeper integration into the ROM itself. T-Mobile USA's Wi-Fi calling comes to mind, but I haven't investigated this at all.