I understand what the black and white stone buttons are. But what is the gray button?
The Black and White buttons will show you Black and White continuations, respectively. But sometimes, there are no local continuations. This happens when the fighting grows into the shaded area from the outside, or the next local move links up the local pattern to a stone outside the search area. If you want to see the games where this happens, use the gray button. Note that the continuation letters disappear, as there are no local continuations in these games. Now just click on 'Show Games' to see what happened.