There isn't any difference as far as using one over the other officially, but the optic yellow is much easier to see when the sun is going down.

The color of the ball has zero to do with HOW the ball hit your thumb. The white ball could have easily done the same thing.

The only difference between the balls may be the cor and compression. Softballs are rated two ways that are stamped on every ball:the Coefficient Of Restitution (COR - pronounced like core) and compression. COR represents how "bouncy" the ball is. The higher the COR, the more bouncy the ball is.Softball compression is a measure of how hard a softball is. The higher the compression, the harder the ball, and generally, the farther it will go and the easier it is to get hurt.
Check the numbers on the ball. If the cor # is .47 or over it will go a lot farther than a .44. If the compression is over 375, the ball is pretty hard. If it is over 500, play third base at the fence.
If you want to get more in-depth, just google cor compression softball and you'll probably get more information than you will ever need!

Lisa and Skip are both correct. Whether the ball has the Optic yellow covering or the white has no bearing on the COR or Compression. There are many variations of COR and Compression, so the ball that hit you may have in-fact been harder, however it has nothing to do with its color.

I am not for sure if you take the balls to your thumb many times while batting or fielding, but either way changing your technique will probably help avoid getting hit so many times in your thumb.

Generally white softballs are slow pitch softballs and have smoothers seams. Yellow softballs are fastpitch softballs and have bumpier seams for getting better spin off the ball when it is pitched.