Answer to Question 1
They are both compact objects, with about the same mass. Both are supported by degenerate matter: white dwarfs by degenerate electrons, and neutron stars by degenerate neutrons.
Answer to Question 2
Absolute visual magnitude of a star is the apparent visual magnitude it would have if it were 10 pc away, and is an expression of the intrinsic brightness of a star. The luminosity of a star is the total energy the star radiates, including at non-visual wavelengths, in one second. Absolute visual magnitude includes only visible radiation.