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I would say that is a semantical distinction. The implication with this submission manual is obviously referring to stuff like 2-in-1 covers like the Slam Dunk ones. Or other Kanzenban releases that have different covers. The volume 1 cover that Vinland used to have, is treated as the first print run. Unlike said Kanzenban new covers.
I mean, the "second" volume 1 cover is a much better representation of the series as a whole. One made under a crunched weekly magazine schedule, the other one on a monthly schedule with time to spare in making it prettier. This seems like one of those arbitrary things where you can just pick the better looking cover since they're both volume 1 lmfao.