Astrological describes things that belong to astrology: the study of where the stars and planets are, how they move, and the idea that those positions might influence people and events. So we talk about an astrological sign, an astrological chart, or astrological advice. The word is an adjective. It does not name the study itself — that noun is astrology — it only says that something belongs to that study. You will hear it in magazines, apps, and casual talk about star signs, and also in more serious writing about the older tradition. Though actually, in everyday life many people just say star sign, not astrological sign.