They are both nuclear reactions. That's just about it. Other than that they are completely different. Fission is the nuclear reaction when two atoms smash the living soul out of each other and split apart, releasing nuclear energy. The other, fusion, involves the same things as fission, expect that extreme heat and pressure is required for it to happen. Instead of splitting each other apart nuclear fusion fuses atoms together into another compound/element, while releasing about 10 times as much energy as nuclear fission.