Tear gas that you hear about on the news, in the form of CN or CS, is often used by law enforcement when they are faced with a combative crowd. The tear gas is launched in the form of grenades or aerosol cans so that the liquid becomes an aerosol. Both CN and CS are irritants -- they irritate mucous membranes in the eyes, nose, mouth and lungs, and cause tearing, sneezing, coughing, etc.
Pepper spray is an inflammatory agent that causes inflammation in the eyes, nose and mouth. Its effect is more debilitating, but you have to hit someone with it directly for it to be effective. This makes it more useful for self-defense against an individual. It is also useful against attacking dogs and bears.