Question

What is the difference between polarizability and polarisation?

Answer 1

The explanation is as follows.

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.

Now,
We can imagine a hydrogen atom with an electron cloud surrounding the nucleus. If an electric field E⃗ E→ is applied (the arrow means vector) 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 p⃗ p→ can be drawn from the positive to negative charges.
p=qr⃗ ,p→=qr→,
where q is the electric charge and r⃗ r→runs from the positive to negative charges. p⃗ 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.p⃗ p→ for the example of the H atom in an electric field, would be given by p⃗ =αE⃗ p→=αE→, where αα 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 p⃗ p→. For a dielectric material with many atoms, each with a p⃗ p→ of their own, we could define the polarization of that material as the dipole moment per unit volume.

Hope it answers your question.
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