I had been thinking about this more. Comparing two sentences again:

  • Jack ran to the bottom of the hill, but Jill wasn’t there.
  • Although Jack ran to the bottom of the hill, Jill wasn’t there.

In the latter, I see how the sentence is more united. It’s clear that Jack ran down the hill to find Jill. Whereas in the first sentence, Jack could have run down the hill for an assortment of reasons. It only occurs to us afterwards that it was to find Jill.