What are the theoretical and/or practical differences between shooting with different lenses at same focal length? For example, if we are shooting with a 24-70mm f/2.8 lens at 70mm focal length vs same focal length with a 70-200mm f/2.8 lens, assuming identical quality of optics and camera settings, will there be any difference in the image produced?
A perfect lens would give the same exact results but there is no such thing as a perfect lens. Even so, this would only be true when focused at infinity. At closer distances, there is shift in focal-length that depends on the lens design. So with two different lenses, one may shift differently than the other.
Practically, you will certainly see a difference, not just between a 24-70 and 70-200 but two 24-70 or two 70-200. There is sample variation in lenses far more than in sensors. I wish they could build lenses with the same precision as sensors but they cannot yet or not at prices anybody but NASA can afford.
The labelled focal-length is also often rounded. Some manufacturers go with even numbers, multiples of five while some have used half-millimeters. So a 24-70mm, could easily be a 23-69mm or 25-72mm when measured, again with the focus at infinity.
You might find some information by looking at a recent video on YouTube by ThatNikonGuy. Here he specifically addresses "focus breathing", but you may be able to see some other differences as well.
The focal length of the lens is typically rounded to a nice number. If memory serves, Nikon's 24-70 is actually 24-68 mm. Many (most?) lenses are not exactly the focal length they claim to be, but they are very close to it.
"Focus breathing" is another consideration -- where the focal length of the lens changes depending upon the distance to the subject. Macro lenses always exhibit this behavior when focused at close range, superzooms typically do, too. Nikon's 70-200 f2.8 VRII suffers from this pretty severely, with the 200mm end of the lens coming down to about 135mm.
So, yes, there is a practical difference between what the lens claims to be and what it actually is. Usually, the difference is pretty small. Also, if you can determine where your preferred focal lengths are you may find that missing some range could be something you don't miss.