If you want history, frigate in its original term in the Age of Sail, describes a ship with one line of guns. More powerful Ships of the Line or Man o Wars can go up to 3 or 4 lines of guns. The US Navy of the Revolutionary period kind of bent the rules a little, with frigates like the Constitution with 2 lines of guns.
With only one line of guns, frigates, particularly on the hands of the French and Dutch, dominated the seas and were the bane of the English, who also adopted the concept. Compared to multideckers, the frigates had a much lower center of gravity and were much easier to handle in the open ocean and in rougher seas. While they lacked the sheer power of the multideckers, frigates made up more than that in seaworthiness and maneuverability.
The operative modern definition of the classic sailing frigate today would be "cruiser".
In fact, that's how it stayed till the seventies. In the fifties and sixties, USN "Destroyer Leaders" or DL, effectively cruisers, were also frigates.
The term had its reform in the seventies when Frigate was changed to DE or Destroyer Escort, which is smaller than the standard destroyer "DD". That was how the "modern" definition of frigate came to be.
The Europeans, particularly the French never adopted this modern definition and stuck to the classic definition. So large ocean going warships that are in effect cruisers, are still called Frigates, and given sub classification like Frigate 1, 2, 3. Thus no surprise they got 6000mt plus frigates - its just in line with their classic definition.
