I was thinking about the role of vise jaws and parallels this morning and came to a painfully obvious fact that I have missed all of these years. The fixed vise jaw, when in proper alignment, is on the XZ plane. The top of this jaw might be parallel to the XY plane but doesn't have to be so.

The ways of the vise should be on the XY plane. When one or more ground parallels are placed on the vise ways, their tops are also on the XY plane.

The movable jaw simply applies the clamping force and is likely not parallel to any plane. It is designed to tilt, rise, and/or fall so it comes in contact with the part which is likely not square.

When I bolt in soft jaws into my vise, it is essential that the soft jaw attached to the fixed jaw sits on the ways. Otherwise, it can (and did) slip down when tapped with a hammer. It is best to use either oversized or slotted holes so there is no chance of the attachment bolts supporting the jaw.

The soft jaw on the movable jaw should not be trusted. I was recently burned by this one. This jaw will rise off of the ways as it applies clamping pressure.