The friction between skates and ice is called Kinetic Friction, more precisely, Sliding Friction. This is the type of friction that occurs when two objects slide past each other. When the skate's blade passes through the ice, Sliding Friction is formed.
Ice and skates also form Static Friction. this occurs when the skates are not moving on the ice. The Static Friction between the skates blade and the ice is very low so this allows the skates to easily move on ice.