Rome Attractions Pass

There is only one pass, the Roma Pass and it's quite difficult to break-even. The Omnia Pass is a just a Roma Pass sold together with an overpriced Ticket for the Vatican Museums purchased on your behalf.

You don't need a pass to avoid the ticket lines, just get tickets in advance on the official sites. Do not trust any re-seller promoting "skip the line tickets". Above all, do not trust English-only websites reselling tickets for Italian museums. There is a reason if foreign companies don't try to resell those tickets to locals and cater only to foreign tourists.

I'll back up Dario here: IMHO the Omnia Pass is very overpriced - I've never seen anyone recommend that one - and the Roma Pass is hard to break even on. It's also lacking its former convenience factor as some of the attractions require advance reservations even if using the pass, and others may highly recommend doing so. You may as well just buy tickets at the same time.

https://www.romapass.it

From the FAQ section 7.1 under "Reservations":
https://www.romapass.it/en/FAQ/

Some museums require reservations for Saturdays, Sundays and holidays
by the day before to respect the social distancing. However, booking
is required in many museums even on weekdays. It is therefore highly
recommended to check the access/booking rules and the opening hours of
every museum you wish to visit. For the Colosseum, Foro Romano and
Palatino, the Borghese Gallery, Mausoleo di Augusto and Palazzo
Valentini (Domus Romane), the ticket reservation is required, even on
weekdays. It is highly recommended to book at least 10 days in
advance. You can make a reservation even if you are not in possession
of your Roma Pass card yet, always providing the name of the Roma Pass
holder.

Instructions follow for how to book reservations if using the pass at the attractions listed above.
The pass doesn't cover anything at the Vatican, and a 72-hour pass only covers entry to 2 consecutive attractions in the RP museum/attraction list. The 48-hour card only covers one. There are (usually small) entry-price reductions on additional museums/attractions.

While it also covers local bus, tram and metro use (but not to/from the airports), the historic center is reasonably compact and more fun to walk. For the few times you may want a bus or metro ride, it's probably just as easy to just buy a few individual 1.5 euro tickets and tuck them away until needed. If you are still interested in this one, be SURE and read all the not-so-fine print on the FAQ page, OK?