Why in finite difference we characterize pdes as elliptical, parabolic or hyperbolic but not in Finite Volume. Thanks

You can use both FD and FVM for solving any type of equations. The classification of pde's has nothing to do with FD and FVM.

I think classification of pdes play role in finite difference b/c a big details of classification of pdes are available in all finite difference CFD books but not in Finite volume CFD books. I want to know if the classification of pdes play role in Finite Difference so why not in finite volume. Thanks

The fundamental difference is that with finite difference methods, you solve the differential form of the equations (via Taylor series representation of the derivatives), and in finite volume methods you solve the integral form of the equations (via control volume approach).

As Praveen said, the classification of PDE's is independent of this. Classification of PDE's simply provides insight into the behavior and characteristics of the system.