Standard gauge, sure. And I guess railroads may have shared terminals in smaller cities or towns. But in larger cities different railroads did have different passenger terminals.
I don't know about freight terminals or links between the terminals of different lines. Maybe somebody else has more information.
Certain large cities were blessed with a multitude of passenger terminals (Chicago once had seven). Of course with most of the stations scattered, this was simply a curse for the passenger connecting through the city on lines with different terminals.
Chicago retains four terminals scattered around the periphery of the Loop, plus Els and subways, and you have to walk (or cab or bus) among them if the Loop is not your destination. There has been (mostly idle) talk in recent decades about a rapid-transit ring connecting the stations, but it's simply going to be too expensive, at least in this cycle of the Universe.