Just like in our world, different places have different languages in Runeterra.
Xayah and Rakan come from the same region in Ionia, so they most likely speak the same language. But Nautilus would probably not be able to communicate properly with Xayah, since Bilgewater and Ionia are seperated.
We got examples of the different languages through teaser videos:
https://www.youtube.com/watch?v=2rpfHB1LU80&t=110s
Urgot's login has the sons of Ur chanting in the background. They are using an old Noxian dialect.
https://www.youtube.com/watch?v=e47AEBnu9SQ
While the text is in English, the song itself is sung in a different language. We got told that this is how ancient Freljordian sounds like.
I hope we will get examples for the Piltovian/Zaunite tongue some time in the future.