Classifying things is the starting point for almost all scientific fields – from flowers to fundamental particles. Once one has classes the next step is to find subclasses, and then sub-subclasses. Finding correlations between different classification schemes, then, often leads to significant understandings.
Neutron stars are not stars in the normal sense. They are remnants composed entirely of neutrons left after a star larger than the Sun, but not too large, explodes as a supernova at the end of its life as a star. There are different types of both neutron stars and supernovae.
Consider neutron stars first. When a star whose inner core is more massive than the Chandrasekhar limit – about 1.4 M⊙ (M⊙ denoting the mass of the Sun) – exhausts its nuclear fuel it collapses as a supernova because it is too heavy to support itself through degeneracy pressure. If the material remaining after the explosion is less than about 3 M⊙ (the Tolman–Oppenheimer–Volkoff limit) the remnant is a neutron star. Otherwise the result is a black hole. Typically, the total mass of the progenitor of a neutron star is in the range of 5 to 15 M⊙.
Since a neutron star can no longer release energy from thermonuclear reactions, it may radiate very little electromagnetic energy. Consequently it may be rather difficult to detect, like a black hole, unless it’s a member of a binary system, so that there are visible gravitational effects on the companion.
However, some neutron stars may have energy sources that allow them to emit electromagnetic radiation at wavelengths all the way from radio to X-rays or even gamma rays. If the neutron star also has a strong magnetic field, such emissions may be observable in periodic pulses occurring at frequencies from a thousandth of a second on up. In this case the neutron star is a pulsar.
There are different types of pulsars too, depending on the energy source.