To Crobato:
The "Seccond generation" in common western practice is the "starfighter generation" which covered the first radar/AAM supersonic fighters like the MiG-21, Mirage III, F-104 Starfighter and J35 Draken. Third generation is described as the "phantom generation" which was clearly the next step from these (but not as big step as the on between third and fourth). Planes included to the third generation are F-4 Phantom, Mirage F1, MiG-23 and J37 Viggen and ofcourse J8II.
That is not what I know about Western parlance. The planes you described as "second generation" are nearly as equally technology and performance level as the "third generation" you mention. The technology change is only evolutionary not generational.
There is no change in doctrine, for one. Supersonic interception is top priority. The engines are still turbojet. There is no leap in aerodynamics, other than the variable wing concept, but the Phantom, the J37 (which uses fixed canards like Mirage III based Kfir), the Mirage F1 and the J-8II don't share that.
Relative stability is another feature in generational change, and a major one when it comes to maneuverbility. Mirage F1 and III don't have that, but 2000 has.
The differences between various generations cannot to be determine just blindly focusing on some design features without thier context. For example Mirage III and Mirage F1 features alot of similar aerodynamical features and even the same genration engine but are still considered to belong to different generation. Draken had 1st gen. Engine (Avon from Hunters) but was still the best 2nd generation fighter ever existed.
And the context of which you have failed to explain how. Unfortunately, there is no major doctrinal change between the Mirage III and the Mirage F1, the latter can only be described as the latter half of the 3rd generation while the Mirage III as the first half of the 3rd generation. The Starfighter itself was deployed concurrently with the Phantom, in fact, in the sixties, right when the Phantom was already in service, the Starfighter was considered quite an advanced fighter.
On the other hand, there is a major doctrinal change on the Mirage 2000 that was a result of the conflicts fought by 3rd generation planes---Vietnam War, Six Day War, Yom Kippur, and Indo-Pakistan conflicts. There is a renewed emphasis on maneuverbility for example, as well as low altitude performance and subsonic acceleration.
Generational differences is _about_ major design issues plus doctrinal context. Just like fifth generation is defined by supercruise and stealth.
Altough J8II may be one of the lesser third generation planes, it still is a third generation and there is clear and logical step in chinese aviation industry when it moveed from direct copies to somewhat indegenious design. All factors favours that J-8 and J-7 belongs to different generation.
There is never, never one mention in any PLA or Chinese literature that described the J-8II as a new generation fighter.
Argument aside, no one thinks that the J-8 belongs to a new generation above the J-7. The engine is literally the same, both use the WP-7 and later the WP-13 engines, and even the Kunlun. There is no fundamental difference in the aerodynamics, seem to work on the same principle, delta wing complete with area rule Coke bottle principle, same you see with the fifties Delta Dagger.