Pittsburgh Basement Flooding: Seepage, Stormwater or Sewage?

The floor is wet, the water is more than a puddle, and the first question has nothing to do with a mop. Did the water come out of the ground, or out of a drain? Pittsburgh basement flooding can arrive both ways, sometimes during the same storm.
Looking at the water will not settle it. This post covers where water gets in, what public sources admit about telling the origins apart, and what to assume meanwhile.