How did they come up with the state/territory thing anyway? I'm not sure if any country other than USA uses this distinction.
I believe it was a reworking of an earlier coring mechanic: If a province was overseas (ie. different continent than your capital, not close to your capital, and not connected by land) then it cost significantly less to core but also provided fewer benefits. IIRC, if you wanted to make trade companies, then they also had to be "overseas". At the time, the way I got my WC as Ottomans was to create a vassal Persia that blocked-off India and everything further east, which made the cost of coring everything vaguely manageable. The state/territory system seems like a development of this earlier feature.
As for the naming, well, it's actually fairly common in former British colonies. Eg: India, Canada and Australia. I'm not too familiar with the political structure of India but, for Canada and Australia at least, "territories" usually have much smaller population and have fewer rights at federal level. It's not a big jump to see how this nomenclature could be reused in EU4.