What is exactly showing in the updater?
On my phone is says:
Fairphone Open 18.02.0
and if I enter the advanced mode, I get Android for Fairphone.
If you phone also says:
Fairphone Open 18.02.0 then you are on the open source version of Fairphone.
Android for Fairphone is the Android 6.0 version which comes with Google.
Have a read here for more details on the different operating systems.