Both of these terms have to do with the construction or destruction of atomic nuclei. Energy is released with each of these processes. In nuclear fusion, hydrogen nuclei are fused together to produce a helium nuclei. Hydrogen has one proton in its nucleus, while helium has two nuclei in its nucleus. Energy is released as a result of this process. This is how the sun and other stars like the sun create the tremendous amount of energy we receive, by nuclear fusion. Nuclear fission, on the other hand, is the splitting apart of an atomic nucleus into two smaller nuclei. This occurs with radioactive nuclei, such as uranium 235, which is a very large, unstable nucleus. Of course, energy is released as a result of this process, as well. This is the process employed by nuclear reactors, by having radioactive rods undergo nuclear fission, and heating water into steam with the energy produced. The steam, in turn, drives turbines which are attached to generators, which produce the electricity we need in our homes and businesses.
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Nuclear fusion is the process in which two atoms are joined or fused together. By this process a single heavier atom is formed. For example this is the process through which sun get its energy. Inside sun, two hydogen atoms are fused into one helium atom.
As opposed to fusion, during nuclear fission, single heavy atom is splitted into two or more smaller parts or light atoms. This is what happens in radioactive decay and nuclear reactions.
Nuclear fusion is the process in which two atoms in a nuclei are joined or fused together.
Nuclear fission is the process in which an atom in a nuclei splits into two or more atoms.