The normal force is one component of the contact force between two objects, acting perpendicular to their interface. The frictional force is the other component, acting parallel to the plane of the interface between objects.
Friction tends to oppose any relative motion between objects, acting at the surfaces in contact.
If there is relative motion, the frictional force is the kinetic force of friction.
If there is no relative motion, the frictional force is the static force of friction.
Let's say you're standing still and you then start to walk forward across a flat floor. Which force of friction is involved? Which direction is it?
Because your foot does not slip on the floor, the frictional force is static friction.
To determine the direction think about what would happen if there was no friction. When you pushed against the floor your foot would slide backwards. Friction opposes this, and acts forwards. Static friction is the force that propels you forward.