Despite being very different in nature Both neutron stars and white dwarfs are the remnants of former stars and both emit electromagnetic radiation (light, heat, x-rays, gamma rays) which is left over from the time they were actively undergoing fusion processes.

White dwarfs are the remnants of smaller stars, they are essentially the solid hyper-hot iron core of stars. They radiate heat and light for many millions of years before they eventually cool off. (Note that this will last longer than the universe is old now).

Neutron stars are the remnants of more massive stars. The moment the fusion fuel burns out, there is no force pushing outwards to counteract the immense gravoitational force - and in the case of these stars the gravitational force is strong enough to overcome the repelling force of protons that keeps atoms apart. The force crushes the nucleons together into a neutron soup. This crush generates immense "heat" energy which is being radiated in the form of gamma rays, radio waves and in other electromagnetic spectra until eventually these neutron stars too cool off in the distant future.

Stars that have had even more mass before the fusion reaction stopped, turn into black holes.