How do I make the pattern angle match the direction of the brushstroke? I just want the pattern for my brush to follow my brush strokes. 
How do I make the pattern do the same thing as in the example? (On)
Craig D Jones is almost right, the answer is Rake.

Both sculpting and UV painting both have the same option that will do what I'm looking for. 
The Rake option when checked makes the pattern follow the brush direction.