Yes it is, Keith, and the generators have 3 winding sets to do it. That's how we have 3 separate waveforms and there are 3 hots to the one neutral. The transmission transformers are generally separate, per phase, because of size. That way they are simpler and cheaper to build also.
When it get to the distribution stations and sub stations it's still 3 phase, all the way out into the fields, where it is divided up by selection of conductors needed and stepped down to the voltage needed. It still only take one hot and one neutral to provide a single secondary winding that is center tapped to give household 120/140. Pole pigs may well have more than one secondary winding if they are serving more than one business or residence. But even those transformers are fed generally with a single primary hot. In fact they could stack on secondaries until they run out of amperage, but they would always be single phase like the primary.
I could accept using the term split-phase for what we have, since the 120 outlets really only receive half-wave AC. That seems fair to me because it's half of the complete sine wave that we see on our 240. But I don't recall anyone calling it that.