Heat leaves a heater in three possible ways: convection, conduction and radiation. Most heaters use convection or radiation. The main differences, in practical terms, are the ways the heat is distributed and how long the heat lasts.
Convection heaters warm up air within the heater housing. The warm air rises. As it rises, it sucks in cooler air at the base so a constant flow of air passes over the heating element and exits at the top of the heater. Most space heaters rely on convection to circulate and heat the air in a room.
Radiation is heat transmitted as infrared light. When you stand in front of an open fire and feel the heat, that's radiated heat passing through the air and hitting you. The heat from the sun and from electric bar heaters are examples of radiated heat.
Convection heaters are best for heating up a room and keeping it warm for long periods. When they are switched off the warm air continues to heat the room. Radiant heaters are better for a quick burst of heat, but if you are not close to them, you won't feel much heat.