I should have been more specific. As far as I know, they cannot be used both on the same plane since they are oriented 90 degrees from one another. Back in the day, while using a field camera, I could shift in the vertical and tilt the lens along the vertical. With the TS-E, you can shift along the vertical, but only tilt along the horizontal. Am I missing something?
Yes, you're missing something. As I stated above, it is possible to alter the relative orientation of tilt and shift to one another with the lens - the feature is called TS Rotation (which is distinct from regular rotation). You can shift in the vertical and tilt in the horizontal (or vice versa) OR both shift and tilt in the vertical (or horizontal).
Note that I'm assuming that you rented the TS-E 24mm f/3.5L II
. The TS-E 17mm and the MkII version of the TS-E 24mm have the TS Rotation feature. The original (MkI) version of the 24mm does not, nor do the TS-E 45mm or TS-E 90mm lenses. Note that with those older designs, it is still possible to have tilt and shift in the same orientation, but it requires removing the shift plate (held in place by four screws), turning it 90°, then reattaching it. Keith Cooper of Nortlight Images describes that procedure here
The difference with the TS-E 17 and 24 MkII is that you can make that change on-the-fly, by simply pressing a button and rotating the front part of the lens. Not only can you have them at 90° or parallel, it's also possible to have tilt and shift oriented 45° (or any other relative relationship, if you ignore Canon's recommendation) to one another. The TS Rotation feature is described in the manual.