Stitched vs wide angle geometry

Help me with some photo theory here

Say you stich 3 portrait oriented shots together from a 20mm lens and it works out to be the same FOV as a 10mm lens shot landscape (just an example, not saying that would really equate). Is the geometry and perspective of the shot the same in the sticthed shots vs the wider angle lens? It seems like it should be because you are the same distance away from the subject, but then with the actual camera movement, perhaps it changes some things?

Just wondering if anyone had any experience with this and could explain how it is the same or different.

Not really. If you had a 20 mm Tilt-shift lens with enough shifts to accommodate the 10mm FoV, you'd get the same effect. With three photos from a regular 20 mm lens, you'll typically be changing the angle of the camera, hence of the film plane, for each of the three shots. So the geometry at the edges of the composite will be different from the geometry at the edges of the 10 mm UWA shot. Pivoting the camera/lens combo about the nodal point is more like using a "panoramic" camera with a curved film/sensor plane than using one with a flat sensor plane.

That's kind of what I thought. So since I am rotating the camera a bit, the parts of the frame near the edges are not being pulled in at such extreme angles, hence less crazy distortion - for better or worse.

Bingo!