I believe they are the same. Are you saying that the motor is twisted, so that at the far end (of the transmission) it's offset to one side? Or is it twisted as in "rotated" so that the trans mounts do not sit square with the crossmember?
Since the motor mount tower holes are slotted to ease installation, an engine can actually be twisted inside the towers. I've run into it before on multiple occasions.
One time we noticed the passenger side header hitting the frame where it should not. After looking at things for a minute we realized the engine was tilted (rotated in the towers, not crooked sideways-like). Or from an aero perspective, the engine had "roll" on it, but not "yaw" if that makes sense.
Fixing it was as easy as loosening the engine mounts (transmission was not hard mounted yet) and two of us sitting on the fenders and each grabbing a header. Add a little lift-and-separate and we rotated the engine in the towers to a more neutral position. Luckily for our work the headers then fit better on both sides and no more interference on the passenger side.
So it can be done if it's "roll" but not sure what it would take to correct "yaw" in the mounts. Maybe some defective mounts? Would not surprise me at all considering the state of modern auto parts.
Paul