What is difference between polarization and polarizability and how do we define it? The book of physics that I have, uses the word "polarization" sometimes and sometimes uses the term "polarizability" and I am getting confused. And I even checked the dictionary for the term "polarizability" and it is not even a word in the English Dictionary.
What might be the case here, spelling mistake or conceptual difference?
 A: In short, polarization (the noun) is the displacement of positive charges relative to negative charges in a system (i.e. an atom's nucleus vs its electrons). Polarizability refers to the difficulty with which such a displacement can be achieved.
As discussed in Griffiths Introduction to Electrodynamics 4E, we can imagine a hydrogen atom with an electron cloud surrounding the nucleus. If an electric field $\vec{E}$ is applied across the atom, the electron will be pulled against the field while the nucleus will be pushed along it in the opposite direction. The charges are thus separated and a vector $\vec{p}$ can be drawn from the positive to negative charges.
$$\vec{p}=q\vec{r},$$
where q is the electric charge and $\vec{r}$ runs from the positive to negative charges. $\vec{p}$ is known as the dipole moment and could be thought of as analogous to a moment of inertia-- a measure of the difficulty of torquing something.
$\vec{p}$ for the example of the H atom in an electric field, would be given by $\vec{p}=\alpha\vec{E}$, where $\alpha$ is polarizability-- the relationship between the strength of the field and the induced separation of the charges.
With the dipole moment defined, we can then speak of the polarization of the atom. The polarization is described by $\vec{p}$. For a dielectric material with many atoms, each with a $\vec{p}$ of their own, we could define the polarization of that material as the dipole moment per unit volume.
