Difference between chemical energy and potential energy
There exist many different potential energies. Maybe you would prefer an analogy. For example let's consider an object on a table (a ball, a book or a piece of chalk). It has a potential energy which is not chemical for the moment. It is not visible. It is a hidden energy. It can only be shown if you give the object an opportunity to fall down and to go to a place where the potential energy is lower. During the fall, the potential energy is transformed into kinetics energy (its speed increases). When it touches the ground, the kinetics energy is transformed into heat which is another sort of energy. This gravitational potential energy is equal to mgH, where m is the mass of the falling object, H is the beginning height of the table, and g is a universal constant (9.81 m/s2 on Earth). Before the fall, the object has a sort of hidden energy, which we call gravitational potential energy (or mechanical energy), and this energy could only be expressed if you give the object an opportunity to go to a lower place. The object has a higher gravitational potential energy on the table than on the ground.

It is the same in chemistry. H2 and O2 have a similar hidden energy, which is a chemical potential energy. If you break the bonds H-H and O-O, you need energy to do it. You give energy to the atoms. It is similar to the operation of picking up the object on the ground and put it higher, on the table. If you imagine going back to H2 and O2, you would get the energy you had consumed for breaking the bonds. But now, if you prefer recombining the H and O atoms into H2O molecules, you will get much more energy (much more heat). 

The object on the ground is similar to H2 and O2. When you give it some energy, you can lift it up to the table, or better to a state of separated H and O atoms. But now if the table is just at the edge of an abyss, you can get more energy by letting the object fall down the cliff. In this case you obtain H2O and not H2 and O2. The chemical potential has decreased to a very low level if the final state is H2O. The fall has produced much more heat than the recombination H2 + O2. 

Chemists often use this analogy between height and chemical potential energy (which is usually called enthalpy). They draw short horizontal lines above one another to simulate  different states, as if one line represents the table (H and O atoms), and another one (lower) the level of the ground (H2 and O2). Of course the level of H2O is another horizontal line : much much lower. 

Have you followed me ? Is it what you needed to understand the potential energy ?