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You must be the only one that thinks of it like this... So if someone asked you which mapper you were using you'd respond "mapper 0" because NROM is technically a board???
You guessed it.
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"A mapper is a piece of hardware soldered to a cartridge's printed circuit board that performs address decoding, bank switching, and possibly other tasks."
Yeah this makes the mapper either a hardware chip (like the MMC1) or a set of chips (for example HC161+HC32) hooked in a certain way, which are basically equivalent to a concept. (I think an electric schematic is a concept).
Calling mapper 2 "UNROM" is definitely an abuse of language everyone on NESdev does (incluind possibly me too), but it remains an abuse of language.
There is several different ways you can get the same mapper behavior. In the case of mapper 2 UNROM is only one of the many ways to get mappre 2 functionality. There is also UNROM-style 3rd party boards (Konami, etc...), UOROM, Camerica boards, and probably a lot of other stuff I forgot.
Mapper 2 can also have 8k CHR-ROM, have 4-screen mirroring, have battery backed SRAM, have any size of PRG-ROM, all this the UNROM board can't, unless its hevily modified.
Also mapper 2 is only one of the two mappers the UNROM board can implement, UNROM can also be mapper 180 (replace the '32 by a '08 and gate and the hardwired bank is at $8000-$bfff).
This is why calling mapper 2 "UNROM" is clearly wrong - mapper 2 is not necessarly UNROM, and UNROM is not necessarly mapper 2.
I don't think it's I who made this up it's just facts. I just pointed this abuse of language that's all. The name UNROM is just a random chain of characters Nintendo put on some boards, it doesn't have much meaning anyways.
UxROM is slightly less wrong, but it implicitely exclude for example 64KB or 512 KB PRG sizes, or the additional features mentioned above, which are all possible with mapper 2.
In summary I know this is a big mess but here are my $2 about this. Sorry for getting off topic.