The accepted term is "rotated die error". Either the hammer die or the anvil die can rotate.
As far as misalignments go, you have horizontal misalignments (the usual kind) and vertical misalignments (tilted die errors). Major horizontal misalignments are generally restricted to the hammer die. But once in awhile, you do have major misalignments of the anvil die. These coins are always broadstruck, because you need the collar to break apart or to travel sideways, carrying the anvil die with it. Vertical misalignments are sometimes coupled with horizontal misalignments, especially when the former are severe. Vertical misalignments can be as severe as 45 degrees of tilt, although they're typically much shallower.
We were discussing rotating die errors in coins. If you notice something different without looking really for the fault consider it a premium coin. If the VAM'S create a furor a rotating die error that much more.
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