In the scoring part of this article, it counts black and white stones in addition to territory. I've been playing for a while and I've only ever scored the amounts of territory with the stones captured subtracted from one's score. Is there something I'm missing here?
The scoring used is area scoring, which counts territory plus living stones instead of territory plus captured stones (territory scoring). The results are almost always within one point of territory scoring, so the strategy with either form of scoring is almost identical to the strategy with the other.
In the West many people learn to play go but have no experienced players around to play with. When beginners play beginners they can have trouble at the end of the game determining whether stones are alive or dead. With area scoring you can settle such questions easily by playing the position out until all stones on the board are alive. So for teaching Western beginners area scoring is best.
If you already use territory scoring, don't worry about the minor differences. But if you ever play in an American Go Association tournament, be aware that the AGA uses area scoring.