The studies and real world data thus far show a reduction in _all_ infections, not just symptomatic infection. The trials for approval only really measured symptomatic infection, so it was unknown whether the vaccines prevented all infections (sterilizing immunity) or just symptomatic infections. So the difference is that a non-vaccinated asymptomatic carrier can still infect others as they are _infected_. Whereas the vaccinated person never becomes an asymptomatic carrier in the first place.