Why does the Chandrashekhar limit apply only to white dwarf stars?

Before quantum mechanics were discovered, physicists knew of no force capable of supporting any star against such gravitational pressure. Quantum mechanics, though, suggested a new way for a star to hold itself up against the force of gravity. The rules of quantum mechanics note that no two electrons can be in the exact same state. Inside an dense star, this means some electrons are forced out of low energy states into higher ones, generating a pressure called electron degeneracy pressure that resists the gravitational force.

This discovery was made by Ralph Fowler, who would later become the graduate supervisor of physicist Subrahmanyan Chandrasekhar. Chandrasekhar, however, realized what Fowler had overlooked. The high-energy electrons inside the white dwarf would have to be traveling at velocities near the speed of light, invoking a set of bizarre effects. When Chandrasekhar took these effects into account, something spectacular happened.

He found a firm upper limit for the mass of any body which could be supported by electron degeneracy pressure. Once this limit, the Chandraskehar limit, was exceeded, the object could no longer resist the force of gravity, starting to collapse.

This is because this is the only thing that is measured. There are different terms that are used for the measurements that are used for different types of stars. It just so happens that the Chandrasekhar limit is used to provide the limit for white dwarf stars before the stars become neutron stars or black holes.

The white dwarf usually does not have enough fuel anymore in order to remain bright. It relies on electron degeneracy pressure so that it will not collapse. In the process, the star can become too dense. When it is too dense, it has a higher chance of becoming a black hole after some more time.