Not that it really matters much, but there are indeed two independent divisions within Trenitalia, with different rules for tickets, etc., different personnel, and so on. The normal passenger never realises this until...

What was described as companies to me by the conductor who wanted 50 Euro + a new ticket (then waived both) because I got on an earlier IC from Pavia to Milano is summarized here (in Italian). At any rate, to avoid any kind of trouble punch anything that fits the machine (if working: 1 out of 3 is usually out of service).