Shot blasting
Shot blasting is a surface treatment performed by attacking the surface with different types of ball grits in steel, glass, ceramics, etc. using an air compressor, with no material removal.
Shot blasting enables a wide variety of applications to be performed in many industrial sectors: Ceramics, Foundry, Gears, Steel, Stainless Steel, Mechanics, Small Parts, Plastics, Molds, Turning Shops, Tools and Glass.
Shot Peening is a cold working process which consists of attacking the surface of a metal part with a controlled jet of micro-spheres shot at a high speed, resulting in increased fatigue strength of the part treated.
Shot peening also improves the distribution of surface tensions disrupted from mechanical processes or heat treatments and significantly diminishes the concentration of stresses caused by notching, threading and surface decarburations. 
Other benefits are a higher resistance to stress corrosion and a decrease in porosity. And as a result of the dimples formed, the surface is able to retain oils or other lubricants more effectively.
Shot peening should not be confused with shot blasting, which, by contrast, is a  surface cleaning treatment.
Sand blasting
Sand blasting is a treatment performed to finish, clean or modify a surface by means of an abrasive shot at high speed by compressed air through a nozzle on the piece.
The term “sandblasting” derives from the fact that the first industrial applications of these technologies used sand from the sea or rivers as an abrasive.