How is voltage (potential difference) like gravitational potential energy? What are their similarities
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Voltage is like gravitational potential and not gravitational potential energy. Let me clear out the difference.
Gravitational Potential Energy: it is the energy of a particle due the virtue of its position. Take this example for instance. If you place a particle at some distance from a planet, say Earth, the particle will start accelerating towards the planet. Once it starts moving we say that it possesses kinetic energy. Where did this kinetic energy come from? It is the potential energy which got converted to kinetic energy.
Gravitational Potential: It is the potential energy of unit mass at a point. it just indicates the potential energy of a unit mass (say, $1$ kg). Now if you were asked to find the potential energy of a particle of 10 Kg, you just multiply the gravitational potential by 10 and you get the gravitational potential energy.
Why is Gravitational potential helpful? Gravitational potential can be considered a function of points in space $G(x,y,z)$. Now gravitational potential energy can be written as $U = G(x,y,z)*m$
Also because $\nabla U(\vec x) = -\vec E(\vec x)$
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Now coming to your question, Voltage is nothing but potential energy per unit charge. Mass and charge being analogous. If you place a charge particle near another fixed charged particle, the movable charge will accelerate, much like the particle near the planet. This acceleration will lead the charge to obtain kinetic energy and this kinetic energy comes from the potential energy it had.