I know a lot of people have jumped in already, but no one has come up with the intermediate version I think I'd've probably written (with one variable rename 'cause that's really long):

    def maxWidthOfVerticalArea(self, points: List[List[int]]) -> int:
        x_coords = sorted(x for x, _ in points)

        max_diff = 0
        for x1, x2 in zip(x_coords, x_coords[1:]):
            max_diff = max(max_diff, x2 - x1)

        return max_diff