What is the difference between a leading edge flap and a slat? I always thought that the definition of slat was:

"Lift modifying and adjustable wing element on the leading edge of main airfoil."

and the definition of flap was:

"Lift modifying and adustable wing element on the trailing edge of main airfoil."

However, there are also leading edge flaps, also known as Krueger flaps, and they are located on the leading edge.

What gives these elements the name of "flap"? What is the main difference to slats?
Slats are leading edge devices on aircraft that enable higher angles of attack. Flaps are devices on the leading (Krueger) and trailing edge which increase camber and the depth of the wing. Slats create a "slat" between the slat body and the wing leading edge so the air can pass from the bottom to the surface to hold off a stall to a higher AoA, flaps merely extend it fore and aft and direct the flow downwards for more lift. Both are mainly used in the low-speed situations of take-off and landing.