Why is charge shared between two insulating bodies till their charges are equal, while the charge is shared between two conductors till their potentials are equal?
When we connect two conductors,they immediately starts working as a single conductors which is obvious because their function is to oppose any electric field present inside their surface.As we know potential difference in a conductor is constant because no electric field exist inside the surface of conductor.That is the reason that two conductors try to make their potential difference same when connected to each other. Whereas in case of insulator no such property is depicted and the charge remain in the reason where the charge is present and no such equal charges distribution happens. Hope you like the answer.
Conductors are defined to allow the flow of charge carriers and insulators are defined to prevent the flow of charge carriers.
When two insulators are rubbed together a static charge is built up by the exchange of electrons. If both materials are initially neutral then each electron leaving one material for the other leaves behind an equal positive charge (positive ion) and so the charge on both materials must be the same.
In conductors, the charge can flow and so the like charges will repel each other and so will redistribute in the conductor. In more detail, each charge will move due to the potential of all the other charges and in doing so the electrostatic potential energy is transferred to the kinetic energy of the charge carriers. The kinetic energy is then dissipated as heat through the scattering of the charge carriers (this is why wires heat up when current flows in them). Therefore, the charge carriers will move to minimise the electrostatic potential energy. This occurs when the conductor is an equipotential (the potential energy is the same throughout the conductor). And interestingly this occurs when all the charge resides on the surface of the conductor and the surface charge density is uniform.
For more details on why the charge resides on the surface see this post: Does the induced charge on a conductor stay at the surface?