We will be traveling from Vienna to Prague. Is there a difference between 1st class Regio vs Rail? Regio seems to cost significantly less for a ticket. Thank you!
Our man in seat 61 gives his descriptions here with photos of seating for both operators.
https://www.seat61.com/trains-and-routes/prague-to-vienna-by-train.htm#choose
Is there a reason why you want First Class for this route, as it is wholly unnecessary? Regio is a private rail carrier known for cheap fares. Railjet is a type of train operations by OeBB, the national rail carrier of Austria. Railjet is not a train company.
As Emily already pointed out, there is absolutely no reason to waste money for 1st class for trains in western Europe.
I did an arbitrary price search for the direct route from Vienna to Prague.
OeBB's RailJet (RJ) trains offer cheap "Sparschiene" bargain tickets, down to €21. The price varies with the booking date and number of seats already booked. The earlier you book the better. Tickets are bound to the train chosen. I recommend to spend extra €3 for a seat reservation. (If you are willing to go with EuroCity [EC] trains having one change, same travel time as RJ though, the price will drop to €14.)
RegioJet trains' prices vary between €25 and €32, depending on different factors not known to me. (RegioJet [RJ] has deliberately chosen its name to be confused with OeBB's RJ trains to syphon off as much passengers as possible.)