Is voltage the speed of electrons?

Is voltage the speed of electrons?

No, it's not the speed of the electrons moving within the conductor.

The voltage unit is potential energy per charge:

An example...

Imagine we have a ball of mass M = 10 kg.

This ball exists in a conservative gravitational field (the Earth's gravitational field). If we want to raise it by a height of 1 meter, we must - somehow - supply an X amount of energy, that gives the ball enough speed to move 1m above its surface.

We will give the ball this amount of energy in terms of kinetic energy (speed). So we throw the ball upwards with some speed, and as the ball moves upward, its speed decreases; and its potential energy increases until the it stops and all the kinetic energy is converted to potential energy.

The following picture shows the amount of potential energy for a ball of mass M = 10 kg at different heights above sea level:

But what if we want to make a generic scale?
For any ball of an arbitrary mass, at any height, we can get the amount of energy for every 1 kg in it (Energy per mass):

Now we can say that, at a height of 3 meters above sea level, any object of mass X will have an amount of energy equals 29.4 joules for every 1 kg of mass. This is due to the earth's gravitational field.

Voltage, or electric potential, is the amount of potential energy (joules) that any "charged body" within an electric field will have, for every 1 coulomb of electric charge in it.

Voltage is a property of an electric field.

An electric field behaves a little like a gravitational field. Objects in a gravitational field are pulled together. Drop a stone in a gravitational field and it will accelerate downwards, taking energy from the field.

Electric fields, unlike gravitational fields, have polarity. Drop an electron in an electric field and it will accelerate in the direction of positive charge. The electron does not have a voltage, it has a charge: \$1.6×10^{−19}\$ coulombs.

How much force is applied to the electron depends on the voltage of the positive and negative sides of the field and their distance apart.

That's all in free space. What about inside a wire? The situation there is much more like a tube filled with balls than a free space. Apply a force to the ball at one end and it will push the ball at the other end out. Apply a voltage to a wire and the electrons will move, forcing out the one at the positive end. The amount of force applied corresponds to the voltage applied to the wire.

The key thing about this model is that the force travels much faster than the balls/electrons that are transmitting it - it doesn't require a ball/electron to go all the way through, it just requires it to push its neighbours along.

Take a Real time scenario,

We can take it water as analogy.

Lets consider a overhead tank and a water tap which is supplied from this over head tank.

Now,

Whenever open a tap water will come through this tap.

The amount of water which is coming through is equivalent to the current

At what Pressure is coming, that is voltage