I am looking for a official term that describes all stars that are not neutron stars or white dwarfs. "Still burning stuff stars" or "ordinary stars" are all I have been able to come up with. Is there an official term for stars that are still evolving and haven't "died" yet?
It is tempting to think that non-degenerate stars covers it, since even the structure of the lowest mass main sequence stars are not significantly affected by fermion degeneracy. Unfortunately the cores of more advanced evolutionary stages can become degenerate.
So I would go with nuclear-burning stars, although this in turn excludes pre main sequence stars.
In some ways it is easier to say a star that is not a compact stellar remnant.
Every so often someone will note that a "star" is a ball of plasma that is supported by nuclear reactions at its core, and so technically neutron stars and white dwarfs are stellar remnants, and not stars.
The technical term is therefore "star". And if you think that could be ambiguous then just spell it out: "Stars with supported by fusion reactions"/"Stars, excluding stellar remnants"
My advice would be to not seek a definition that is "official," because official definitions will often not serve the application you have in mind. Just say what you want to say, tailored to that application. We'd like definitions to be instructions for sorting everything that is from everything that isn't, but in practice they actually can't work that way. For example, what is the official definition of a "computer", that works in any context? At one level, the definition of a star should include whatever objects people who regard themselves as "stellar astronomers" study, because it is the commonality among all such stars that unites them. But most "official" definitions of a "star" already exclude many of the objects that "stellar astronomers" study! (The same holds for "planets.") So although official definitions do exist, they are often not what you want in your application. That's why I say, just define what you mean yourself, and don't even try to be "official." For example, if your interest is in stellar evolution, and you are not interested in endpoints because they are not still evolving, then say stars that are still evolving. If your interest is stars that obey an ideal gas law, you might favor a term like "ordinarily gaseous stars," or some such thing. Tailoring to the interest gives a better definition than something "official."