When I was younger, I would go on road trips with my family to Texas. Along the way, we drove down Interstate 10 through southern Arizona and southern New Mexico. Somewhere in New Mexico, we crossed the Continental Divide. On one side of the divide, water flows downhill to the Pacific Ocean. On the other side, it flows downhill to the Atlantic Ocean. Perhaps two drops of water from the same thunderstorm that land just a few inches away from each other could end up in radically different oceans.
In southern New Mexico along Interstate 10, the Divide is apparently flat. I would not guess that there is a divide there, but the sign on the side of the road says there is.
A divide is a (possibly subtle) change in gradient that causes something, over the long run and in general, to flow toward a different (potentially radically different) destination, than it would have before crossing the divide. A watershed is a "gradient regime" (a kingdom of flow?) that leads toward a particular end.
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