It just means the truck has an upgraded trim package, and it seems that there wasnt a "standard" SR5 package, so it could be any variable of trim upgrades... but back in the day (pretty sure it was a wednesday) the S stood for Sport, R was the engine code and it had to be a 5 speed. SR5.
I have an SR5 with a automatic...
But,,, I think it orginally (in the 70s) stood for Sport Ralley 5 speed. I think the term just got re-used over the years