I thought I understood the curve modifier, but after walking through this simple sequence, I'm more confused than I started.
I start with two copies of the same thing. A cube and a Bezier curve. Each cube has a curve modifier with its respective Bezier curve as the curve object.
I then proceed to scale BezierCurve1 by 5x in object mode leaving it with a X, Y, and Z scale of 5. I scaled BezierCurve2 by 5x as well, but I did so in edit mode. The X, Y, Z scales for BezierCurve2 are therefore 1 (not shown).
Now comes the part where I'm confused. I applied the scale on BezierCurve1 and now I (mistakenly?) believed that the two sets of objects should be identical. All objects have their X, Y, Z scales at 1, the vertices are all the same (except for the offset along the y axis) but apparently not so. The modified Cube1 is now stretched in a strange way that I cannot explain.
What is going on here? Why are the two not the same?