It's possible for both the hammer die and the anvil die to be misaligned simultaneously.  Typically, the misalignment seen on the anvil die is small, since the die neck is confined by the collar.  Most of the time, the misalignment on each face points in a different direction.

    This 1966 nickel shows a slight horizontal misalignment of the hammer (obverse) die toward the 10:00 position.  The reverse (anvil) die shows a slight horizontal misalignment toward the 3:00 position.