But they are considered frigates nonetheless with most of the same combat parameters. One must consider that the Grigorovich is more the equivalent of the original type 54 frigate.
If we can be so selective of the type of comparisons that we can make, then calling the type 54b the best frigate ever is obviously untrue as it would be skipping a few challengers. Like the Iver Huitfelt class.
The admiral gorshkov is in no way a destroyer class vessel. Indeed Russia currently have no vessels that fits the 7000-9000 ton weight class.
Displacement is an ancillary measure when evaluating naval combatants and etymological description's even less useful. The most important is outfitting, from sensors, armament, to special missions equipment. In that regard, the Gorshkov is not comparable to the 054 family. So, no, they don't have the same combat parameters except displacement. In fact, they have combat parameters that are almost entirely different which is why I said comparing them directly is folly.
The 054A is a
supporting combatant meant to undertake ASW missions as part of an expeditionary fleet and possesses a decent but rather low-end air-defence suite with limited anti-saturation capability. By contrast, the Gorshkov is not a support combatant and will assume the primary combat role as the air-defence heavyweight in any Russian fleet, as the 052Ds and soon 055s do in a Chinese fleet. The vessels that will support the Gorshkovs are the Grigorovichs and Gremyashchiys so
those are the ones that should be compared to the 054 family. FYI, the Grigorovich's displacement is almost identical to the 054A's, not that it matters very much because displacement gives limited information about a vessel's role and capabilities.