, a stolen base is when a baserunner
successfully advances to the next base while the pitcher
is delivering the ball to home plate
If the baserunner advances to the next base when the ball gets past the catcher, the catcher would be charged with a passed ball and the runner would NOT get a stolen base. (However, if the runner was already attempting to steal a base and the ball got by the catcher or was a wild pitch, the runner WOULD get credit for stealing the base. If he advanced an ADDITIONAL base, that extra base would be the wild pitch or passed ball, and not a second stolen base).
Also, if a team tries a double steal, and one of the two runners is caught stealing, the other would NOT get credit for a stolen base, although he advanced.
In addition, if the defensive team doesn't even attempt to stop a player from stealing a base, the official scorer can rule "defensive indifference", and not credit this as a stolen base. This often happens late in games when the baserunner doesn't really matter to the defensive team (for example, in a 9-2 game, in the 9th inning, the leading team would not care if a runner on first went to second)
The abbreviation used for a stolen base is SB.
Both the major league single-season and all-time stolen base records are held by Rickey Henderson (130 during the 1982 season; 1370 career, through the 2000 season).