I agree with ace here. As a few examples will show how the designation works: Before their TRUMP, the RCNs Tribal-class was classified as DDHs; afterwards, with aStandard-system installed , their designation changed to DDG. The Town-class frigates, although they're equipped with the ESSM, are still FFHs. Similarly, the German Brandenburg-class is a FF, but the Sachsen-class, on an identical hull, is an FFG, because of her Standard system.
I do believe that some ships esspecially a few of the soviet types that weren't/ain't fitted with a Medium-Long range Sam system in the SM-1/2 Class or of Russian/Soviet, Chinese n European equivalents were still classified as FFG, CG, or DDGs because the ships primary weapons were purely missiles esspecially long range anti-ship missiles, the only SAMS fitted onboard were short range Point defence SAMs in the Seasparrow/Osa-MA (Gecko) Class in addition the ship wasn't fitted with a primary large/medium calibre Gun at all.
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"The British Air Farce have droopped their bums on the water works..They have scored a direct hot on the pimps"- British agent/gendarme Officer Crabtree, "Allo,Allo."