Without examining the objects it is not so easy to say, but my first guess would be, the "flat" stripe is set to Shade Auto Smooth (or Auto Smooth enabled afterwards), while the "curvy" stripe is set to Shade Smooth i.e. Auto Smooth not enabled. If this is not the solution, I guess on the "curvy" stripe the Subdivision Surface modifier was placed after the Solidify modifier.
Here is an example for the Auto Smooth option, I've recreated the shapes:
To get the same look for the left one, either select it, then right-click in the viewport and choose Shade Smooth or go to the Object Data Properties and disable Normals > Auto Smooth there:
The Auto Smooth option lets you set an angle (30° by default) above which an edge is considered sharp and will not be shaped smooth anymore. So the top and bottom rim with 90° angles are sharp. If Auto Smooth is disabled, the shading of everything will be smoothed out, even the 90° angles on the border, that's why it looks rounded. This also means, if the stripes were flat and had no thickness, they would both look the same (flat), because then there would be no 90° angle over which the smooth shading would be extended.
And here is the option with the different order of modifiers. On the right you have a thinner light reflection than in the previous example, so maybe this is what happened there: