Air superiority and interceptor in modern terms mean nearly the same thing. The only difference is that the latter is usually left to more high end fighters, since they need the extra performance to penetrate enemy defenses and hunt them on the enemy terms, rather than just neutral air superiority.
I think at the start when there was not that many J-20, they would be the designated interceptor aircraft. But today, there's enough to fill a wide variety of roles.
In 2025, J-20 would still be the go to if say radar finds evidence of F-22 formation over Kyushu, we have to fly there fast to fuck them up. But unlike in 2019, J-20 can not ONLY be spared for that purpose but can be spared for "easier" missions.
And in some years, J-20 will probably leave interception/deep penetration missions to J-36 and only fly alongside as backup if at all. Basically what J-16 does today.
The distinction between interceptors and air superiority fighters is largely a result of legacy technological limitations rather than any conscious doctrine decision.
In the past, due to technological limitations you had to choose to be able to go fast or be manoeuvrable enough to put up a decent dogfight. Think Mig31 vs Su27. This was the result of the failure to achieve the best of both worlds via swing wing designs like the F14 and Mig27 that the worlds fighter design houses decided they needed to pick one at the expense of the other.
That was compounded by the more primitive missile and radar tech of the time where there was a decent chance of opfor fighters being able to sneak up on you, most notably via using ground clutter interfering and notching to flank you while fooling your Doppler radars etc. Worse, even if you did detect the enemy at long range and engaged them, your long range missiles had questionable to poor kill rates against agile enemy fighters, so even then you run the real risk of ending up in a dogfight.
Today, just the advanced in missile and radar tech alone almost makes this distinction irrelevant. Just look at how well the Mig31 has been performing in Ukraine when that is your classic pure speed no turn legacy interceptor.
But the true game changer is supercruise. Which allowed highly manoeuvrable designs to still beat pure speed rockets like the Mig31 in the speed game by having sustained high speed cruise over shorter bursts of higher speed.
But that is all somewhat academic because even though top-of-the-range 5th gens like the F22 and J20 can dogfight with the best of them, you are using your stealths very wrong to find yourself in a dogfight at all.