How many types of star remnants are there?

When stars die, they leave behind remnants, usually compact objects of some sort. What kind of remnant it is depends on the initial mass of the star, and how it met its' death.

There are three types of star remnant include one that’s shell-like, such as Cassiopeia A; another is composite, in which a shell contains a central pulsar wind nebula, such as G11.2-0.3 or G21.5-0.9. The last one is mixed-morphology remnants, in which central thermal X-ray emission is seen, enclosed by a radio shell.

The thermal X-rays are primarily from swept-up interstellar material, rather than supernova ejecta. Examples of this class include the SNRs W28 and W44. Interestingly, W44 additionally contains a pulsar and pulsar wind nebula; so it is simultaneously both a "classic" composite and a thermal composite.

There are also planetary nebulas, black dwarfs, white dwarfs, neutron stars and black holes that would be considered as remnants.

It should be remembered that there are different stars that can become supernovas. There are different explosions that may occur once again, this is due to the type of star available. Since there are different explosions, there are also different remnants that are left behind. It is required that the star should have a certain solar mass so that it can become a supernova.

It is not dependent on how large the star is. Our sun which is considered to be a medium-sized star does not have enough solar masses in order to become a supernova in the long run. If it reaches its peak, it would become a white dwarf and cool down.