The distinguishing technical fact about fixed stars in astrology is that their positions move, and this makes them the one component of a Western chart that cannot ignore precession.
The stars keep their patterns relative to each other but drift against the tropical zodiac at roughly one degree every seventy-two years, because the equinox point from which the tropical zodiac is measured itself moves. Over two thousand years that is nearly thirty degrees, a full sign. Regulus, which sat at the very end of tropical Leo through most of the modern era, crossed into Virgo around 2011, an event discussed at length in astrological literature at the time, since a star read for two millennia as royal and leonine had moved into a sign of an entirely different character. Practitioners divided over whether the sign placement matters at all for a star.
The consequence is that star position tables must be dated, and that astrological references give positions for an epoch. Vivian Robson's book of 1923 remains the standard astrological reference in English, and its positions are now a century out of date and must be adjusted forward, a fact that catches out readers who take its listed degrees literally.
The names carry their own history. Most of the bright stars used in Western astrology bear Arabic names, Aldebaran, Algol, Fomalhaut, Deneb, Altair, Betelgeuse, because the Greek catalogues were preserved, corrected and extended by Arabic astronomers through the medieval period, and Europe received the stars back with those names attached. Ptolemy's catalogue supplied the planetary natures; Babylonian and Egyptian sky lore supplied the older layer beneath that, including the four so-called Royal Stars at the quarters.
Astronomers, it should be said, use the same stars for entirely different purposes and make no claim of the kind astrologers make.