Stars are not Planets

[Mireille_Bouquet]

You're right. According to science, a star and a planet are two different things. It would be a real problem if Final Fantasy XIV was piece of hard science fiction.
...but it's not. It's a fantasy setting that loves to use archaic terms for things, even beyond Urianger.

Historically, planets have been referred to as stars. See: Venus, the Morning Star.

To expand on this, yes modern science is the one that differentiated stars from planets, however past/old science, old astronomy, had the visible planets as "stars that wandered".
Basically, past civilizations saw that most all the lights in the night sky were "static", except some that traveled around over many day/night cycles and seasons/years, yet they referred to all those points of light as stars.
Those wandering stars were called "planasthai" by the Greeks, which evolved into today's "planet".
It wasn't till around the 1630s that planets were "main stream" called out different from stars in the then sciences.
So, in the past, all the points of lights in the night sky were stars, even though some were planets and moons (and some larger asteroids plus comets) and the rest were galaxies (and galactic clusters & nebula) and individual stars.

As FF14 exists in an alternate form of Earth, with it's inhabitants spanning the equivalent of tens of thousands of years in technological development across the various regions and races at the same time, it's not a far stretch to have ones call different celestial bodies all "stars".
So, to the OP, yes star is a valid term for a planet in FF14 megaverse.