You're definetely correct, but it's also a quirk of localizing Japanese into English where translating a word from Japanese has no direct English equivelant (bare in mind I dropped out of my Japanese language course so my knowledge on this subject is very, very rudimentary so if anyone is more knowledgable on this subject and can add or clarify things please by all means do so!), but from what I understand the Japanese use the same word to mean both a planet and a star in the celestial context, as they're both shining objects in the night sky.
In Modern English we have a very specific seperation of meanings between the two (the word 'planet' of course coming from a Latin word that means 'wanderer', based on the astronomical observation that the planets were not in 'fixed' positions and did move across the night sky), but Japanese does not have that distinction. So it's common to simply use the word 'star' to refer to the world itself (this also pops up in a lot of dubbed anime as well for the same reason). Yes it's a bit odd, but it also does enhance the antiquated, even alien, feel, of Eorzea as a setting. It's a part of worldbuilding. ;)
