What is the difference between static friction and sliding friction?

Friction in general, is a force that opposes the motion of an object.

There are two kinds of friction: static and kinetic.

Static friction is the the type of friction that prevents an object from moving, keeping it in static. You can calculate the static friction using the equation: #F_"SMAX" = mu_"S"F_"N"#.
=> Where #F_"SMAX"# is the maximum friction of the object to cause it to move, in Newtons.
=> Where #mu_"S"# is the coefficient of static friction for the object. It is unitless.
=> Where #F_"N"# is the normal force of the object in #N#.

An example of static friction is a car parked on an incline. The friction stops the car from going downhill.

Kinetic friction is the friction that most people associate the word "friction" with. It is the friction that opposes the sliding motion and tries to reduce the speed at which the surfaces slide across each other. The kinetic energy is converted into heat (and sound) energy.

You can calculate the kinetic friction using the equation: #F_"K" = mu_"K"F_"N"#.
=> Where #F_"K# is the friction of the object to keep it in motion, in Newtons.
=> Where #mu_"K"# is the coefficient of kinetic friction for the object. It is unitless.
=> Where #F_"N"# is the normal force of the object in #N#.

An example of kinetic friction would be a ice sliding across ice and then coming to a stop.

Hope this helps :)