Both. The batter is out, and there was no voluntary release after the catch.

Then, by rule, you would HAVE to call the batter Safe on the uncaught ball. You cannot consider this as "no voluntary release after the catch" because that would make it a no-catch.

That was the point of my response. The ball came out of the glove when the fielder attempted to tag the runner, not when he attempted to make the catch. The catch essentially ended as soon as the fielder turned to begin his chase of the runner. Even if the ball had popped out of his glove as he was running after the runner and before he lunged to make the tag attempt, the catch would still be legal.

Incorrect.

Then please explain to me what I'm missing when I read this in OBR 2.00's Definition of Catch:

In establishing the validity of the catch, the fielder shall hold the ball long enough to prove that he has complete control of the ball and that his release of the ball is voluntary and intentional.

Complete control of the ball is necessary for a catch. Although a voluntary release is always proof of complete control, sometimes a catch is established before there is any release of the ball.