Often times im working on an image like this, and when i click with either the Wand or Bucket tools, they only work on pixels that are vertically or horizontally connected to the same index color.
I wish there was a boolean checkmark on the top of the screen, beside “Contiguous”, that read something like “Diagonally”. Then, when i used either of these tools, it would also affect/spread to the same color diagonally with a single click, like this: