How do the terms polarity and polarizability differ from each other?
In my opinion, polarity is the degree of ionic character in covalent compounds and polarizability implies towards degree of covalent character in ionic compounds. Am I correct?
Polarity and polarisability are almost entirely unrelated.
Polarity refers to the distribution of partial electric charge in molecules (or even materials). Or, more technically, the degree to which a molecule has a dipole moment (which relates to its inherent electric field). Some molecules, like benzene, are non-polar as they have no net dipole moment; others, like nitromethane, have a strong dipole moment. Polarity is a fixed property of the molecule that doesn't depend on the external field.
Polarisability refers to the degree to which the electron clouds in a molecule or atom can be influenced by an external electric field. Everything, polar or not, has a polarisability. Crudely (i.e. simplifying a lot) you can think of it as the degree to which electrons are held tightly in the atom or molecule. So xenon atoms are fairly polarisable compared to helium atoms as their electron cloud is more spread out and less tightly bound. Water is very polar but a lot less polarisable than hexane which is non-polar. Bulk substances have complicated polarisability that depends on the crystal structure and may be inhomogeneous.
Polarity is about the ground state electron distribution; polarisability is about how that distribution changes when subject to an external electric field.