OK, this all makes sense. But why does it matter? Am I as a programmer going to make mistakes if I try to write programs in a "what" manner instead of a "how" manner? Is there some other, better distinction that I should be making?

Are you really saying that what matters is abstraction, and that we would be better off thinking about higher vs lower levels of abstraction instead of the more subjective what vs how? I think I might agree with that, but then you do get into the problem of deciding which of two pieces of code is more abstract, and I think you are going to end up with the same problem all over again of it depending on your assumptions.

Oh, and thanks for the interesting comments!