ignoring Lathe,
In the modern era the traditional lines between ship types Patrol Ship, Coastal Corvette, Frigate, Destroyer,and guided missile cruiser (with Light Cruiser, Heavy Cruiser, battle Cruiser and dreadnought all gone the way of the dodo) have all blurred. Typically today its the systems, armament and role that classify a surface combatants not the weight. The German navy is a fine example most of its "Frigates" would fit nicely as Destroyers, and are used by other navies as such. Its mostly the doctrine and the way that they are deployed that decides there term.
Another example is the US DD21 class which in many ways fits the classic light cruiser more then traditional destroyer. Or the LCS classes which as "Littoral Combat Ships" sound more like Patrol boats or Corvettes yet the final product is far closer to a traditional frigate.
Basically the terms in modern context is more.a term of convenience... Just ask the Japanese Maritime Self Defense Force who as we all know classify not one but two helicopter carriers as destroyers.
So calling it a frigate even if it displaces as much as a destroyer is fairly normal.
Well, my post was less oriented around what the name of the type of ship it is rather than how large and capable (and expensive) the ship is, and the role of such a ship.
In other words, the fact that they're considering replacing their current relatively "low end" 3600 ton ships with 7000+ ton ships, which are the same as their soon to be "high end" Hobart ships which are also 7000+ ton in displacement, is very confusing.
I mean, it's not without precedent per se because the OHPs/Adelaides were previously the high end of the RAN's surface combatant force and displaced only a few hundred tons more than the ANZACs, however it's still eyebrow-raising that they would consider elevating the entirety of its future surface combatant force to be in the 7000+ ton class.
I would have expected a class of maybe 5000 ton ships to replace the ANZACs and act as the low end to the larger and more capable Hobarts.
But instead, the proposals are coming out with a ship that may be as large and as capable as a Hobart, but to be procured in a large run of 8 rather than 3... and I can't help but wonder if RAN can afford it.