The Wikipedia article does note that there are psychological differences between the two score systems but it does not appear to place much significance to that. But psychological reactions to a voting system will surely influence how people vote. Differences in presentation, such as whether to ask a simple Approve or Disapprove question of the voter for each candidate rather than asking the voter to assign a numerical score could quite possibly make a profound difference in how people vote. In the past, discussions of score voting rarely if ever considered using negative scores. With only three scores, a choice like (0, 1, 2) or more likely, (1,2,3) would be used for illustration. And the possibility of a voter leaving blank the selection for a candidate was mostly just ignored, probably for considerations of mathematical simplicity.
Care is required in examining the claim that BAV is just the same as score voting using (0, 1, 2). Mathematical models of them may be the same, but mathematical models are abstractions that often ignore features simply because mathematicians deem as irrelevant. These two systems are not the same when it comes to computing vote tallies, they are not even the same with respect to being completely defined real-world voting systems, they are not the same with regard to ignoring unmarked preferences and they are not the same with respect to the psychological impression the ballot makes on voters (and we learned in the 2000 Florida experience with butterfly ballots how ballot appearance can distort voting). But it does remain true that aside from these real-world considerations, mathematically they might well be considered the same.
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