Both fission and fusion are nuclear reactions that produce energy, but the applications are not the same. Fission is the splitting of a heavy, unstable nucleus into two lighter nuclei, and fusion is the process where two light nuclei combine together releasing vast amounts of energy. read more...
Nucrear fission
Nuclear fission is that which generates energy from the process of breaking atoms into smaller atoms. The nuclear fission occurs on an unstable isotope of atoms (usually an atom with the same number of protons, but has a varying number of neutrons) The most popular fission nuclear reactor is Uranium-235. If the nuclear reaction of the Uranium atomic fission is written down the chemical reaction would be like this:
U-235 + n ----> Ba-144 + Kr-90 + 2n + about 200 MeV
U-235 + n ----> Ba-141 + Kr-92 + 3n + 170 MeV
U-235 + n -----> Zr-94 + Te-139 + 3n + 197 MeV
Nuclear fusion
While the term nuclear fusion reactions is the incorporation of atomic nuclei to form on one heavier nucleus of the atom, and followed by the release of enormous energy. This fusion reaction is experienced by the Sun. Where the isotopes of Hydrogen atoms such as Tritium (Hydrogen-3) and Deuterium (Hydrogen-2) join under high pressure and temperature which will form the isotopes of Helium and neutrons. The reaction of nuclear fusion you can read [here](https://en.m.wikipedia.org/wiki/Nuclear_fusion)
Conclusion
From a little discussion of the difference above it can be concluded that both fission and fusion nuclear reactions both produce energy but have a much different process of occurrence. In fission reactions is the breaking of heavy atoms into smaller atoms, whereas in fusion reactions is combining small atoms into heavier atoms.