Various recipes will tell you to use a square or a round pan. So
here I am wondering if there is any reason why there is a
difference. For example, a 9 inch round or an 8x8 inch square have
about the same area:

9 inch = 63,6 inches square

8 x 8 inch = 64 inches square

So, if I make a cake in an 8x8 inch pan when the recipe calls for a
9 inch round, is there any real difference? Certainly not in area.

I can understand if I baked something in a 16x8 pan when it called
for an 8x8, but the above example is what I'm thinking of, when
it's so close.

Can anyone offer an informed opinion on this? I rarely bake so
this sort of thing throws me.