Your guesses are correct - but note also that many logs don't split into nice semi-circular sections. If you have a big log you may split it into quarters or fifths or whatever.

By exposing more interior wood they do dry out quicker when split. And they burn better as medmech says, because bark and the exterior layers don't burn as well.

Splitting wood is only "fun" as long as you don't HAVE to do it - as long as it's recreation, so to speak, it's ok. But it's dang hard work without a hydraulic splitter!

Rgds,
Chris W.