When the catcher drops a pitch that would be the third strike, the batter has struck out, but is not out, and is free to run to first base and be safe even though she has struck out, unless first base is already occupied, in which case she has struck out and is out, unless there are already two outs, in which case she has struck out but is not out, and the batter and all runners are free to run and be safe, even though the batter has struck out with two already out. In all cases the pitcher will be credited with a strikeout, even though some of those strikeouts will not be recorded as outs.
There, I hope that clears up any confusion.
There, I hope that clears up any confusion.