Yes, they do.  They seem to use different orbital, gravity, geoid, TAI, etc 
models.  Trying to merge fixes from different systems leads to all sorts of 
problem,  particularly at nuttery levels.  I've seen reports that GPS and 
GLONASS fixes can be off well over 50 meters when referenced to  the same map 
model.
----------------
> Meanwhile it would not surprise me if each GNSS system gives a slightly 
> different position and a slightly different time than GPS does.               
>                           
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