How come the acceleration in electrical interactions between charges are different? When talking about the accelerations during free fall, they are all the same regardless of mass. However, after reading through the textbook and watching videos, I still do not understand how acceleration is different in electrical interactions? Is it because the masses are different between the particles?
 A: Since force = mass*acceleration therefore acceleration =force/mass. When you calculate force on a charge particle in an electric field, you simply multiply the charge of the particle by the electric field:
Force (vector) = electric field strength (vector) * charge
F=E*q
You can substitute E*q in for force in the earlier equation:
Acceleration = E*q/mass
Therefore the charges acceleration is also affected by the field strength and is therefore different to just gravitational interaction
A: Because mass is the cause of force and a measure for opposing acceleration, a mass that 2 times as big will experience two times as much force but at the same time offer two times as much resistance to it. This is called the equivalence between inertial mass and gravitational mass.
If we increase the charge of a mass the electrical force on it and the acceleration increase both, if the mass stays the same. If we increase both the mass and the charge, the acceleration on a body can be the same. If we put 100 electron charges on a massive body, and put it in an electric field, the body accelerates the same as a body with 200 charges and twice the mass. 100 electrons together (not on a body but just together) accelerate the same as 200 electrons as tha mass is automatically doubled. A proton will accelerate differently from an positron. Their charges are the same but their masses differ.
A: TL;DR The electrical interactions are much more sensitive to distance between the charges than the gravitational interaction in case of a free fall.

The second Newton's law tells us that the acceleration is a consequence of a net force acting on a body (particle):
$$\vec{F}_\text{net} = m \vec{a}$$
where mass $m$ is assumed to be constant.
Free-fall is a consequence of a gravitational force between the falling body and the Earth
$$F = G \frac{m_e m_b}{r^2} = m_b g \tag 1$$
where $G$ is the gravitational constant, $m_b$ is mass of the body, $m_e$ is mass of the Earth, and $r$ is distance between the two bodies. Note that the acceleration $g$ depends on the distance $r$ which is not constant during free fall, but for all practical purposes could be assumed constant.
The electrical interactions are due to the Coulomb force
$$F = k_e \frac{q_1 q_2}{r^2} \tag 2$$
where $k_e$ is the Coulomb constant, $q_1$ and $q_2$ are (signed) magnitudes of the charges, and $r$ is distance between the charges. Notice the similarity between the two forces in Eq. (1) and Eq. (2)! However, the electrical interactions are much more sensitive to the distance.
A: 
I still do not understand how acceleration is different in electrical
interactions?

Basically, it is because, unlike the gravitational force, the electrostatic force on a particle is independent of the mass of the particle.
The electrostatic force $\vec F_{ES}$ exerted on a charge $Q$ by an electric field $\vec E$ is given by
$$\vec F_{ES}=Q\vec E$$
Note that this force is independent of mass. On the other hand, the force of gravity near the surface of the earth is given by
$$\vec F_{g}=mg$$
depends on the mass.
For example, the magnitude of the electrostatic force is the same for a coulomb of negative charge (electrons) or positive charge (protons). But the acceleration of the positive charge, from Newton's 2nd law, will be much less than that of an equal amount of negative charge due to the much larger proton mass.
Likewise, two objects with different mass and having the same amount of positive or negative charge will experience different accelerations.
Hope this helps.
