if i purchase a timed train ticket say between florence and rome from the trenitalia.com site - does that include a reservation? i know simple question and its probably obvious - just checking
Yes your ticket will have your name on it and the assigned car and seat number listed, just like when you buy an airline ticket. All seats on those trains are assigned. You can pick before you checkout where you want to sit and no one else can sit there. It happens sometimes that you will find someone mistakingly sitting in your seat.
Here is more info with pictures
https://www.seat61.com/trains-and-routes/frecciarossa.htm