A stumping generally happens when the bowler has deceived the batsman with some combination of length, speed and/or spin and has enticed him to come out of his ground to play a shot - as such, it involves an amount of skill on the part of the bowler so they are credited with the wicket.
A run out means that the batsman has hit the ball and decided to run, but for whatever reason there wasn't actually a run there. The skill here comes from the fielders and whoever breaks the wicket, and no significant input from the bowler - as such, they're not credited with a wicket.
