All three spices contain anethole, the molecule behind the anise taste, and the trade names overlap. In Chinese, star anise is 八角 or 大茴香, “big fennel”, and fennel is 小茴香, “small fennel”. In French, star anise is badiane or anis étoilé, aniseed is anis vert and fennel is fenouil. In English, “anise” can mean star anise or aniseed.
Japanese star anise (Illicium anisatum) looks similar to Chinese star anise but is not a food. That is another reason to put the botanical name in every specification.