# Different types of densities? Regular density vs free electron density?

I know the density $\rho$ is $$\rho=\frac{m}{V} \quad \bigg [\frac{\text{kg}}{\text{m}^3}\bigg ] \tag{1}$$ But in solid-state physics an another type of density if the free electron density $n$ $$n=\frac{N}{V} \quad \bigg [\frac{\text{units?}}{\text{m}^3}\bigg ] \tag{2}$$ And in this link, $n$ written as $$n=\frac{N_A}{M} \cdot \rho \quad \bigg [\frac{\text{units?}}{\text{m}^3}\bigg ] \tag{3}$$ where $N_A$ is Avogadro's number and M is the molar mass.

Questions:

What is the electron density $n$?

What is the relationship between the "regular" density $\rho=m/V$ and the electron density $n$?

And also, how can $n$ be written as both equation (2) and (3)?