Yes these files are about switch on prediction (HotFix) not about GPS Accuracy.
Reason: Data in files gets over-written after a while with the true data from the GPS.
If you convert 1300 to Jap Hotfix is not as Good as EU/US and takes longer for FIX, But it's still usable.
I think this is the case with 37>34 Real 34 is a newer device after all.
Also I think Real 34 is a bit over-optimistic by declaring 3M Accuracy all the time even when weak satellite signals are present.