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The term helium star is naturally used for stars with some helium-related characteristics (in some cases due to a decided lack of hydrogen) but the term has been used for various such scenarios. Perhaps the common current usage is an O-type star or B-type star with stronger-than-usual helium spectral lines.
A different use of the term is for a white dwarf that has begun helium burning through merger with a binary companion. A third, older use, was as a synonym for B-type star.
The term extreme helium star (sometimes shortened to helium star) is used for stars with nearly no hydrogen, helium making up most of the star. Such a star burning helium in an analogous manner to hydrogen burning in a main sequence star is said to be on a helium main sequence (helium MS). The presumption is something removed the hydrogen, such as interaction with a binary companion, or an extreme stellar winds. They are PV Telescopii variables (PVTEL).