Radioactive decay, in which a nucleus spits something out, changing itself into a different kind of nucleus.
In the case of radioactivity the reaction is spontaneous. Fission and fusion can be done on purpose, to release energy. This energy can then be used for different things, for example to make steam (as in a nuclear power plant). It can also be used as energy for a bomb.
Nuclear reactions differ from chemical reactions in that they do not need a catalyst. Radioactive decay also cannot be stopped, sped up or slowed down.