While boiling and evaporation both produce water vapor, they are very different. Evaporation is a surface phenomenon, and it happens regardless of the temperature of the water. You even get evaporation from ice, which is why food gets "freezer burn", and why after a long vacation you may find that the ice cube trays are half empty. At the surface, water molecules are constantly moving into the air, and back to the water. If more leave than return, you get evaporation.

Boiling happens all through the water, not just at the surface. It only happens when the temperature of the water is high enough that the vapor pressure of the water is the same as the pressure of the surrounding air.