libnds has fixed the datatypes of pretty much all registers and have moved to the GBATek nomenclature for the BG-related registers. The list has been updated to match the libnds v1.3.1. of
[/note]The state of register names for NDS homebrew is a bit of a mess. First, there are the GBATek names. Since GBATek is considered the source of GBA/NDS information, it would make sense to adhere to those names pretty closely. But, of course, that's not how actually is in the de facto library for NDS homebrew, libnds.
libnds has two sets of names. This probably is a result of serving
different masters in its early days. One set uses
Mappy's nomenclature.
That's the one without the REG_ in front of it, and
uses things like _CR, and _SR. This is
one you're most likely to see in the current NDS tutorials.
The second set uses GBATek's names (mostly) plus a REG_
prefix. If you've done GBA programming, these should feel quite
familiar.