Nuclear energy is produced by a process called nuclear fission, where a heavy atom such as Uranium-235 or Plutonium – 239 is bombarded by electrons splitting the heavy atom into two or more atoms. Simultaneously energy is also released, and neutrons are also released. In nuclear reactors, the speed of these electrons is controlled and we can thus get stable nuclear power.
In contrast, in nuclear fusion, two or smaller atoms combine to get a larger atom and energy is released. Solar energy is produced in the sun is one produced by nuclear fusion of two hydrogen atoms. Once two hydrogen atom at high temperature combine, they form inert helium gas and release energy and one neutron. The process goes on.