On highest mountains

A correspondent writes to ask about the difference between tallest and highest in such sentences as Everest and K2 are the two tallest mountains in the world, which he has found on a BBC site. He quotes Michael Swan as an example of a grammarian who says that it has to be Mont Blanc is the highest mountain in Europe and not . . . the tallest mountain, and is understandably confused.

Usage is undoubtedly blurred, because we frequently see such listings (very common online) as 'The Tallest Build...