Question

What are the similarities and differences between gravitational and electric fields?

Answer 1

There's plenty of similarities and differences, but I'll point out probably the most significant of each:

Similarity: Inverse square laws
Both of these fields obey "inverse square laws". This means that the force from a point source drops like `1/r^2`. We know the force laws for each are:
`F_g = G (m_1m_2)/r^2 and F_q = 1/(4pi epsilon_0) (q_1q_2)/r^2`

These are very similar equations. The fundamental reason for this relates to continuity laws, since we can imagine integrating across the whole surface and finding a constant only proportional to the enclosed volume (Gauss's law), but I will assume that is above your paygrade.

One result of this is that both forces have energies that shrink like `1/r`, since we integrate the force across a distance to get the energy.

Difference: Masses aren't negative
The major difference between these two is that gravity is never repulsive. If you put two like charges together, you will always get repulsion. On the other hand, all masses are seemingly attractive, i.e. there is no negative mass like there exists negative charge.

If we wanted to be pedantic, we should write the definition of forces with `F_g = - G (m_1 m_2)/r^2`, but that doesn't matter here.