Potential energy encompasses various forms beyond just gravitational potential energy, including elastic, chemical, electric, and nuclear potential energy. The discussion clarifies that potential energy is energy stored due to an object's position within a force field, and it is part of the broader category of mechanical energy, which is the sum of potential and kinetic energies. However, chemical energy, while a type of potential energy, is often not classified as mechanical energy due to its quantum nature. The conversation also highlights the distinction between conservative forces, which store energy, and non-conservative forces, which dissipate energy. Ultimately, the consensus is that all forms of energy can be related to mechanical energy in some context, but the terminology can lead to confusion.