Both Ishgardian and Sharlayan forms of astrology are essentially real-world forms of divination being elevated to the point of legitimacy through magic. It's just that while Sharlayan astrology is formed of more personal fortunes and so has healing components to it to boot, Ishgardian astrology is aiming much broader, using the stars to make greater predictions about the future.

Essentially, Sharlayan astrology is a direct fortune telling (hence why its main job mechanic is a tarot spread), Ishgardian astrology is horoscopes. And Far Eastern geomancy is Feng Shui.

That said, I think we're generally meant to believe that all three of them work, it's just that in the case of Ishgardian astrology, there is a marked difference between 'works' and 'useful'.