What is the difference between the electrostatic potential energy of a charge immersed in an electrostatic field and the potential energy between two charges? 

>Is there a connection between the two? Are they the same thing expressed in different ways? What does change? 

I mean, the two expressions are quite different, one is the potential energy for a single body, the other is a potential energy between two bodies. Moreover, one is zero at no distance between two objects, the other is zero at infinity (always assuming a certain constant $C$ is $0$). 

>What is an intuitive explanation for this? What do these energies represent?

Could the same be applied to gravitational potential energy as well?

Thanks!