Answer:
Boiling is the "rapid vaporization of liquid" when the liquid is heated at the point where the pressure of the vapor is equal to the pressure exerted by the atmosphere in the liquid.
So during the boiling, the vaporization of the water is also occurring but is a little bit more complex.
Some questions that you may ask your friend to differentiate those two phenomena are:
Which one is used to cook things like pasta? (boiling)
in which process, a liquid is transformed into a gas? (evaporation)
Which one includes the other? (boiling)