The Triumph class was created in response to the absolute trouncing the Terran Navy got during The Third Interstellar War. She was the first of the "solid hull" style designs the Terran Fleet adopted in response to the League's adoption of them in IW III.
The Triumph was very much a design of it's time, small and able to run down other ships in normal space, with little consideration outside of that. She was designed to fight not against the League, but the civilian ships of the Confederacy. Smaller, faster ships were needed for the new war, and the Triumph excelled at her task.
Because she was so cheap of an design and filled a really useful niche of a patrol boat and general purposed armed craft, that thousands were made. They were so cheap and plentiful recent Terran designs now use them with a mothership, greatly increasing their utility without increasing the overall cost that much more.
This has lead to the interesting fact that the Triumph might be the single most plentiful hull in human history. She's been updated, modified, refit and redesigned to fit new roles, both military and civilian.
Primarily a complete system overhaul with lessons learned from both the class and the new Fleet Doctrines in general.
Focused on an extensive engine overhaul, still in use to this day.
Almost all Triumph classes (including decommissioned but not scrapped hulls) were updated to this refit at the time, and everything manufactured after got this refit by default.
This refit was primarily weapon systems, reactor and CIC overhaul. She was made more power efficient, with better tracking, and better support for more modern missiles. This particular refit is considered the more desirable for people looking to refit a Triumph, as it doesn't have any of the post Charlemagne"nerfing" done in the name of safety.
Only ships built with Refit II were ever given Refit III, all others were simply built to the new specification. There was a large number of older Triumphs that had been upgraded to Refit II that were mothballed instead of upgraded.
This refit was focused on fleet-wide changes after the Charlemagne Disaster. The main focuses were reactor safety systems and subspace detection systems. It was deployed to all currently commissioned Triumphs, but no real effort was made to refit any decommissioned or mothballed hulls, unlike Refit II.
The primary focus of this refit is to allow Triumph class ships to better dock and interface with motherships. This new refit is primarily seen in newly manufactured ships and hasn't been widely deployed among the fleet yet.
The Triumph was originally designed to fight against (relatively) fast civilian craft in normal space, breaking up the swarm tactics the Confederacy was using in the Fourth Interstellar War. She excelled at that role, but after a few incidents, it was determined that a small squadron of Triumphs were shockingly effective against small to medium sized capital ships, including a few hard-won victories against Light Cruisers.
After Refit II, the swarm tactics were retroactively embraced and now it's rare for a single Triumph class to be assigned anything. Triumph Captains work very closely with each other and squadrons of Triumphs tend to be very tight knit, very well trained, and experts in using their small ships to punch well above their weight class.
The Triumph is primarily used as a patrol craft, and as a counter to other LCS or small sized capitals. They are deployed in areas where there's a lot of small craft expected, or where there's a need for a moderate amount of firepower with a minimal amount of overall cost.
This is basically the Hummer of the RFI Universe, and we love our dumb little ship.