What is the difference between nuclear energy and chemical energy?

Chemical and Nuclear energy are different. Chemical Energy is potential energy that can be converted to other forms, usually heat and light. This is energy when bonds form. The stronger the bond the more chemical energy that can be converted.

Nuclear Energy is the energy that can be converted to other forms when there is a change in the nucleus of an atom from a) splitting of the nucleus b) fusing two nuclei to form a new nucleus. Nuclear energy can be both potential and kinetic.