I am experiencing the very same problem on Linux/Windows (from GOG).
Interestingly the names of planets and the stars are the same, but on whoever joins the game the name of the the system and the star do not match. So that's where it is off.
We tried both expansion and non-expansion. We also made sure we both have the latest version, redownloading from GOG.
Could it be that there is some minor difference in the compilation or some data file where some synced ID or something does not end up matching?