The entire bleeding interceptor / striker etc argument has gotten out of hand.
Let's put the division clearly:
Fighters -> primarily intended to destroy other aircraft
Attack / Bomber Aircraft -> primarily intended to attack ground targets.
Within the attack / bomber aircraft family, you see attack planes like the A-10 Thunderbolt II which is intended to attack ground vehicles, or general attack aircraft which can attack a variety of surface targets, and often have some self-defense ability against fighters.
Bombers, on the other hand, are intended to deploy vast amounts of munitions at altitude, often not for precision strike, and often have very long ranges to boot.
You also have aircraft which are classified as fighter-bombers, such as the JH-7. These are attack aircraft that are intended to conduct warfare at stand-off distances, but often have better self-defense ability than attack aircraft against other aerial threats.
Now, let's discuss fighters.
First, most fighters these days are multi-role (omni-role is the new marketing phrase), meaning that they can conduct a variety of missions ranging from interception to ground attack. Second, you have general basic categories of interceptor (intended to attack support and bomber aircraft), air superiority (intended to destroy enemy fighters), and strike (enhanced ground attack ability).
The funny thing is, with 4th generation (international) and 5th generation aircraft, the lines between these categories have blurred. For example, the F-16 was set up as a light air superiority aircraft. As it evolved, its avionics improved, its load capability was reinforced, and it became more of a strike aircraft. But if you put in a fully-modern F-16V vs a F-16A, the F-16A should lose because it has BVR disadvantages and even WVR the F-16V has much more thrust.
Or take a look at the MiG-31, for instance. On paper, it's an interceptor. But the difference between the MiG-31 (4th generation) and MiG-25 (3rd generation) is that the MiG-31 can actually dogfight to an extent, having sufficient advantages against third-generation fighters in terms of speed and no marked differences from 3rd generation fighters in terms of maneuverability. It's demonstrated 18 degree / sec turns. Moreover, in BVR, it has a decided advantage over all 4th generation air superiority fighters, with the challenge being for its missiles to actually hit the air superiority fighter.
The point is, when we say the J-16 is a striker, it doesn't mean that it's worthless vs an air superiority aircraft. It's still fairly competent, and against its same generation peers, while it'd be wasteful to deploy it in such a role, it can still defend itself and maybe even push the attack. The distinguishing factor is simply that it's reinforced for a larger air-to-ground payload than the J-11, and when you consider the technological differences between a J-16 and a J-11A/B, the J-16 can win easily because it has better BVR ability.
In fact, in the 5th generation, we can argue that an air superiority role is actually limiting. If you consider the F-22, for instance, the F-22 is abandonware in part because it has no considerable ground attack ability. It can launch a few bombs from its shallow bays, but it can't pack anti-ship missiles or long-range anti-radiation missiles.
The F-35, in contrast, can do much of the same the F-22 can (be stealthy, launch AAMs), but can load more powerful air to ground missiles. The only thing the F-22 truly has over the F-35 is that the F-22 is capable of high-speed interception missions that the F-35 can't do due to a functional speed limit of Mach 1.3-Mach 1.6.
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In conclusion, the labels are bloody meaningless once we get to 4.5 and 5th generation aircraft. No one optimizes aircraft for a single role anymore, and even when an aircraft has a "single role" affixed to it, you can't expect its capabilities to match similar aircraft in the role; c.f. J-16 striker can intercept, while the F-16 striker can't.