Yep, rifling twist was changed when the name of the cartridge was changed.
Anything labeled .244 will have the early twist, anything marked 6mm will have the later twist and be able to handle the heavier bullets.
The 6mm is a great cartridge.
Had Remington handled the introduction a little differently, as in putting the correct twist on it when it was first released, I think it would have had a VERY good chance of becoming the standard American 6mm instead of the .243 Winchester.
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