What are Uses of thin airfoil and thick airfoil?
Thick, cambered airfoils such as the Gottingen, Clarke Y and Davis are the most efficient airfoils up to speeds where Mach number becomes critical.

Lift is determined by the lift formula:  

$Lift$ =  1/2 × Coefficient of Lift × Air density × Wing Area × Velocity$^2$

Coefficient of Lift can be further broken down into Angle of Attack and Airfoil type.

So a smart designer picks the most efficient airfoil and the least amount of area required
to lift a given weight.

Now time to choose.  By virtue of Bernoulli, the highest lift to drag ratios are achieved by accelerating air over the top of the wing.  This is where thick wings shine, much to the amazement of aircraft designers 100 years ago.  Thick wings also have gentle stalling characteristics, helping make the Fokker D.VII a real hit in 1918.  The thickness also enabled internal cantilever construction instead of bracing wires, paving the way for higher speeds until...

Higher airflow velocity above the wing approached trans sonic speeds, which lead to an increase in drag.  This forced designers to give up the top lift and use bottom lift, where the airflow is slower. That lead to the "supercritical" wing for high subsonic cruise.  Super critical wings feature a very "flat" upper surface.  Note airliners drasticly increase camber for slower phases of flight with retractable slats and flaps.

Supersonic aircraft wings are thin to avoid drag, but can create lift with a swept leading edge, much like a paper air plane.  This type of lift is called vortex lift.  As seen from the formula above, Velocity is squared.  This means that at high speeds, the wing need not be as efficient to generate the desired lift, as seen in designs such as the Concorde.

Of course, with very little weight, like a paper airplane, it works too.