Regular sails actually work similarly to a wing, in that pressure differentials on either side create a force we call lift on a plane, rather than simply being "pushed from the back" by directly catching the wind. That's why a sailboat can go in almost any direction regardless of which direction the wind is blowing.
Watching bleeding edge yachts sail is always interesting. Hydrofoils achieve speeds greater than 3x wind speed though their stability doing it is a bit alarming.