Prime Titans are cosmetic reskins of the default Titans. and must be bought with real money. To offset any potential pay-to-win factor of the Primes, the Prime Titans have no functional differences to their base-game counterparts, and simply serve to add an extra layer of cosmetic customization. The weaponry employed by Titans does not get any kind of change, with the exception of the Broadsword employed by Ronin, which changes in appearance only, being more lean.
Also, Prime Titans have their own unique Termination that no other Titans have, including other Prime Titans.
Prime Titans were not available at Titanfall 2's launch and were instead added through staggered updates, these being Angel City's Most Wanted, Colony Reborn and Monarch's Reign (or, every other update). Two Titans were released in each update, in the order of Scorch Prime and Ion Prime, Northstar Prime and Legion Prime & finally, Tone Prime and Ronin Prime.
Currently, there have been no announcements of a potential Monarch Prime, though it is likely one will be added down the line.