If exponential growth keeps going until you run out of people to infect, then you get to everyone in both scenarios.

What actually changes the total number of infections, is that when enough people are non-infectious by either vaccination or prior infection, the remainder no longer get exposed.

The other society scale effect is that the slower infection rate (even in the absence of the primary benefit of the various vaccines) means the integrated utilisation of finite healthcare resources is spread out over time, so the instantaneous usage is lower, and as many places were at or above capacity during the pandemic that would also save lives.