Distillation means gasification of water and then making water from water vapor. Chlorination is disinfection of water by using chlorine.
By distilling water, you can get rid of salts, some impurities, solids, etc. that are found in water. Distilled water is used in laboratories. It is also used for disinfection of water although it is not preferred at large scales. Distillation requires energy and time.
Chlorination is also a disinfection method. The main advantage of chlorination is that a chlorine residual is formed that provides secondary disinfection of the treated water after leaving the water treatment plant.