BM4 refers to the “Balanced Mod [4th edition]”. It’s broadly similar to the original Global 1940 with some minor modifications and additions to make it more balanced.
If you’re trying to use one of these for Pacific 1940 2nd edition (no modifications), then you’ll have to do a few things to make it work. You’ll have to ignore the European nations and all the new additions. Keep in mind that the US has significantly fewer national objectives in the Pacific-only map as opposed to the European map (tip: If a national objective mentions a territory not on the board, it’s a good indicator that it’s not in the Pacific-only version). You’ll need to still consult the rules to account for all the changes though.