Frecciarossa

All fast trains have reserved seats.

The Base price is the Base price- what you will pay day of or without any discounts.
Economy and Super Economy are discounted tickets with restrictions- usually non-refundable, non-changeable.

You seem to have a lot of questions about train travel in Italy
This site should answer all your questions.
https://www.seat61.com/train-travel-in-italy.htm

Or click on "offers" at this site to see explanations of all the various ticketing options for Freccia and IC trains.
https://www.trenitalia.com/en.html

There’s a limited number of Super Economy tickets which is what I always buy weeks ahead of time to obtain the best price. But, they’re not refundable, so know your exact date & time. That’s why I just purchase my first arrival day train, if applicable, when I’m near the train station - because I don’t know which time I will be at the station to leave.

In a nutshell:
Frecciarossa has 6 classes of seats. In increasing order of comfort (and price):
STANDARD
PREMIUM
BUSINESS
BUSINESS SILENZIO (must stay quiet like in a library)
BUSINESS SALOTTINO (small conference rooms)
EXECUTIVE

All seats above are reserved, but they are sold at the following fares:
BASE=full price/No discount. Always available.
ECONOMY=about 25% discount over base price. Only a limited number of seats are sold at this fare in any class. So the longer you wait, the higher the chance the offer is gone.
SUPER ECONOMY=Work similarly to the Economy fare but with about 40% discount over base price. So these tend to sell out really fast.

Warning: once you buy a discounted (economy or Supereconomy) ticket on a specific train in advance, you are locked in. You can’t make changes or get refunds in case you change your travel plans. They are totally non refundable.

There is now an option on the Trenitalia website to add a "ticket refund option." It's under the area where you add the passenger details. The option costs either 1 euro or 2 euro per ticket, depending on class of service. Pretty cheap for a little peace of mind.

I just looked for this on the app and didn't see it. I guess there's some advantage to being an old luddite and needing to do these types of things on a big screen with a keyboard. :)
Thankfully I noticed this on the first ticket I purchased (for five people!) because I accidentally selected the wrong day and had to get a refund, which occurred within minutes.

You still have to make a change at least 2 days in advance and you get credit for 90% of the ticket cost.

You still have to make a change at least 2 days in advance and you get credit for 90% of the ticket cost.

and it's still better than Italo's equivalent option. You get only 80% of the ticket cost with them

you can also find lots of travel vlogs on Youtube about Italian trains, all sorts

@Sam - I got a refund for the full cost of my tickets (but not the 10 euros I paid for the "make it refundable" option).

From the site:
With the “tiRimborso” (Ticket Refund) option, Economy and Super Economy tickets, Young and Senior offers, and Me&You and Insieme offers are now refundable!
The “tiRimborso” option costs €2 for Super Economy, Me&You and Insieme offers and €1 for Economy, Young and Senior offers on all sales channels.
The amount will be credited to the same payment method you used for your original purchase.
The option is valid for Frecciarossa, Frecciargento, Frecciabianca, Intercity, Intercity Notte and Eurocity tickets on national routes. It cannot be purchased for tickets with a total cost less than or equal to €10. The amount paid for the “tiRimborso” option is non-refundable and does not contribute to the calculation of the refundable or compensable amount.
For the Me&You and Insieme offers, the “tiRimborso” option must be purchased by all members of the group and refunds will only be granted on condition that the request is made at the same time and for all passengers. A partial refund of the offer for only some members of the group is not permitted.