Potential energy is the capacity of an object to do work. This can take many forms. Chemical potential energy is a good example - coal doesn't look like it has a massive amount of energy in it, but set fire to it and it burns for hours. The potential energy is stored inside the C-C and C-H bonds within the mixture of hydrocarbons, which are broken in the combustion reaction and then reform in new ways to release that energy.
A box on a high shelf has gravitational potential energy. Anything that is in a field has potential energy due to its position. Work is done against gravity in the Earth's gravitational field to raise the box from the ground to the shelf, and this energy is stored as GPE. When the box is pushed off the shelf and accelerates to the ground due to gravitation, this GPE is converted to kinetic energy mainly. This is the capacity to do work being realised.
A stretched spring also has potential energy. Consider the motion of stretching it with your hands, it involves effort to do so because you are doing work against the restoring force the spring produces due to Hooke's Law (F = -kx, for spring constant k). This work is stored as elastic potential energy, and is released when the spring is released.
In conclusion, both have potential energy. I hope this helps :)
