The stands are different. However...
The height of the 20" Cinema Display's stand is 10" from desktop to the horizontal hinge. The 23" ACD's stand is about 0.75" taller.
The hinge widths are similar (3.5"), so it is likely that you can install a 20" ACD on a 23" ACD stand.
There is plenty of clearance (> 3.7") from the desktop to the bottom of the 20" panel, so it is also quite likely that you can mount a 23" ACD on a 20" ACD stand, as long as you don't mind the 23" ACD sitting 0.75" lower on the desk. The unknown is if the spring within the 20" ACD stand's hinge is too weak to maintain the angle of the 23" ACD at all positions.