Question

σ vs ρ. What is the differences between these charges densities?

Answer 1

$\sigma$ is known as surface charge density. It denotes the charge density when charge is distributed over a surface (i.e., a two dimensional surface. e.g. on the surface of a sphere.) Mathematically it represents the the charge on a unit area of surface.

Quantitatively  

VO=0

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$\rho$ is known as volume charge density. It denotes the charge density when charge is distributed inside a volume. e.g. when charge is distributed inside a sphere. Mathematically it represents the charge on a unit volume of space.

Quantitatively  

p=Q/V