1. Did you confuse HQ-10 with something else, like HQ-9? HQ-10 is a short-range system, no? While HQ-16 is longer-ranged (medium).
2. Yes I agree these 7 ships (why did you say 8?) are now second-line. That's more like the case as later frigades, both Chinese and western, have grown bigger and more capable. But saying AFTER being refitted they are no longer DDGs is simply counterintuitive and IMHO doesn't make sense. If that is how categorization works the PLA should have re-classified all those older ships as frigates as soon as 054As came in.
3. I know the 051B at least has better communications and command capabilities than 054As. Weapon-wise it is now not too different from the latter.
Yup I meant HQ-9.
I meant six ships --- the four Sovs and the two 052Bs --- once all these ships are done with their refits and re-incorporated into the future. They will move from the first line to the second line, and you will need ships to replace them for the first line. The 051B makes it seven, but that ship has already been "processed" into the second line, and already has a first line replacement. When I meant 8 ships, that was the six older destroyers, plus the two 054 frigates that now appear headed into a major refit, likely a full on conversion to a 054A. The whole point is that the PLAN is going to gain 8 054A like ships, plus the 051B, you got nine, on top of the real 054A.
Term "DDG" doesn't have context anymore. The old Type 052 and even 051s are DDGs just because they have missiles, even short ranged ones like HQ-7s for air defense. What's even more counterintuitive is to call both the Type 052 and Type 055 both DDGs, which gives you an impression that somehow they are equal in name, but the air defense capabilities are vastly different. There needs to be better categorization by functionality, by level of air defense.
Growth in size of European frigates means these ships now even overlap the Sovs and 051B, and borders the 052C/D in tonnage. I don't really think the Europeans are following the modern adage of "frigate" any more but has reverted to the original concept of the frigate during the Age of Sail where the frigates are effectively cruisers.
First line --- 051C, 052C, 052D, 055
Second line --- 054A, 956E/EM converted, 052B, 054 converted, 051B
Third line --- 052, 056, 056A, 053H3.
Term origin. Destroyer comes from shortening of Torpedo Boat Destroyer. During the Pre-Dreadnought era, the Torpedo Boat came to be and threatened the Battleship. The result is the introduction of a new ship aimed to destroy the Torpedo Boats and protect the Battleships, serving escort to them. It should be noted it has nothing to do with size but purpose --- during WW1, German torpedo boats were as big as British destroyers and are practically the same class of ship. When the Airplane and the Submarine came, you got two new platforms that carry torpedoes, and the protective work of the Destroyer is extended to these. Then the Torpedo is replaced by the guided missile, the plane became the jet, and guns can no longer protect ships alone from jets and missiles --- the Carrier has replaced the Battleship as the capital ship to protect --- so the destroyer needed missiles to do the same job of protecting the fleet. Missiles need big space, and this caused a massive explosion of the Destroyer's size as the type entered the guided missile era.
During the Age of Sail, frigates represent single line ships, meaning one gun deck, as opposed to Ships of the Line that have multiple gun decks. Unlike the Sloop or Corvette whose range is tied to the port, the Frigate is much more independent and could sail the seven seas, the minimum ship that is considered fully ocean traveling. Frigates became the most important warship during the Age of Sail, and whose purpose in modern times would be the equivalent of cruiser. The use of the term ebbed by the age of steel warships, but the British resurrected the term for use as a destroyer escort, which created this strata of the Frigate being between the Destroyer and the Corvette.
So why are the Europeans calling such large warships, frigates? I think Europe is in the gradual process of discarding the 'destroyer' in name and looking to collectively phase the term out one by one. Maybe it has something to do with European nationalism, politics, and identity, with the frigate a throwback to the glory days of European navies in the age of sail, when they dominated the seas. 'Frigate' is now a term of purpose --- an independent multi-role warship --- not a destroyer-lite. The Europeans are not going to rename their old destroyers frigates, but they simply stopped calling the newest ship classes 'destroyer' and refer to them as frigates, even if these frigates are as big, or bigger, and equal or heavier in armament than their previous destroyers. I think the Type 45 and the Horizon class maybe the last ship classes in Western Europe to still be called 'destroyers'. The Type 26 frigate is about as heavy as the Type 45 destroyer and is better armed offensively. It has reached to a point that frigates might be divided into subcategories within 'frigate', where you have first line, battle frigates like the FREMM, Type 26, the F100/110, the Iver Huitfeld, De Seven Provincien, and then second line, intermediate or small size frigates, like the FTI, the PPA and the Type 31. In relation, the Type 054A is closer to the intermediate group, even if its more heavily armed.
But of course, what the Europeans are doing, does not affect what the US, China, Japan, S. Korea, and Russia will continue to do and how they categorize their ships. Each will have their own way to suit their own purposes. The point is, names like destroyers and frigates no longer have meaningful context, or any reference in weight. They have become politicized and branded. You can call a ship a destroyer even if its a cruiser, a helicopter carrier is being called a destroyer, and ships that are functionally cruisers, frigates.