Countersinks feature a very unique geometry that cuts a "countersink" and a "counter bore" in the same hole. These rivets are manufactured to designed to take high Tensile loads.
A flush Tension head rivet is used primarily on external metal surfaces where good appearance and the elimination of unnecessary aerodynamic drag are important.
A flush Shear head rivet takes advantage of a countersink hole; countersunk or flush rivets are used extensively on the exterior of aircraft for aerodynamic reasons such as reduced drag and turbulence.