The Milky Way Galaxy is a spiral galaxy whose arms are literally full of life. The arms of our Galaxy are the locations in which new stars are formed. The life stages of a star, however, are what categorizes stars.
Protostars are not exactly full-fledged stars. They are only gaining enough luminosity and temperature to move into the next stage of star life.
Main sequence stars are perhaps one of the most important types of stars because there are more main sequence stars than any other types. The main sequence stage lasts for billions of years. For instance, our own Sun has 12 billion years to spend as a main sequence star. Currently, it is almost halfway through. Main sequence stars are luminous according to their masses. The more massive they are, the more luminous they are. And, what defines whether a star is a main sequence star is its energy source. Hydrogen-burning (converting hydrogen into helium) stars are main sequence stars.
Red giants are stars that are past the main sequence phase of a star's life. Red giants are big, very luminous, and very red. Red giants are burning up their hydrogen more quickly than main sequence stars. They spend only a little time being red giants than being main sequence stars (only a few billion years).
White dwarfs are red giant stars that have contracted so much and have burned most of their hydrogen so that they are not as nearly luminous as they once were. White dwarfs generally are very small, but they are massive (meaning that their mass is compressed to a very small space).
Black holes and neutron stars are special types of "stars." Black holes are very massive, and nothing escapes them, not even light. Some have speculated that time travel is possible through black holes and wormholes, but this is only speculation, since nothing can travel faster than light. Neutron stars appear to "pulse," even though they are just rotating on an axis, and their radiation (the light that they emit) seems to go "on" and "off."
Supernovae are not exactly stars, but explosions and remnants of stars. Supernovae help to form new stars.
There are also star clusters; these clusters may or may not have formed together. Some loose star clusters will move away from one another. For instance, it is thought that the Sun may have been part of a loose association of stars, and gradually moved away.
All of these stars are apparent in the Milky Way Galaxy, as in any other galaxy. We can see the concentration of stars, interstellar dust and gas in the arms of our Galaxy, and know that many kinds of stars exist there.