Diana isn't an assassin. She's a bursty fighter mage

Ap assassins are reliant primarily on abilities usually if not always. This limits builds and stuff.

AD assassins can do sustained and burst. They can also build weird utility items and benefit more from them all spammylike.

Aka known as ap assasin

Only by people who don't understand the difference. Many of which will be crying about how OP [insert new champ name] is every 2 weeks because they don't understand the game's design.

Edit:
Diana is highly dependant on autoattacks throughout the game
Diana has a defensive ability and a utility ability with no damage on it rather than more ways to dish out the pain or gank or whatever
Diana has to faceroll like a mother****er to get the kind of burst she needs or she has to use her autoattack based magic damage.
Her gapcloser is targeted and isn't strong enough to be considered special unless you manage to land her Q
Her Q is a heavily broadcasted skillshot with a channeltime. Like its meant to be dodged

Diana is not an assassin, she is a figher mage. She goes in tanks some damage and does some damage, pins you down, and does some more damage. Against some she can just go in and burst them but she isn't terribly effective for bursting as scary as she looks doing it when it works out.

Fizz is a tanky fighter burst mage. What are they both classified as? Mages. What do they excel at doing? Getting in and getting out or chasing down an enemy. The only real diffrence is the utility diana can bring to a teamfight.

And about kha zix...hes a great example of game design right?

fizz is not a mage, he is a fighter assassin.

fizz dives in, bursts, and rather than tanking everything he actually dodges it and gets back out to persue runners. You'll notice that where other fighters tank, fizz dodges.

He is not a mage even though he does do magic damage

Kha zix is a wonderful example of game design. However his role currently is highly limited in the face of teamwork and he is also dependant on teamwork. This is the cache 22 of the assassin champion type.

To be fair, AP assassins can't turn into the lochness monster endgame. I'm talking auto attackers who can crit 100% of the time at the attack speed for quadruple digits. Although i agree some of them snowball too well considering their kit: aka Akali.

Fizz is a fighter assasin that scales off ap. In fact all of his significant damage comes in a form of an ability, much like a mage. It woulds be safe to call him a mage but he fits extremely well into the ap assasin category. Like you said he tends to jump around and get out which really fustrates me as he can juke quite easily without sacrificing a whole lot.
But since diana is natrually tanky she can go for an offensive build but still kill anyone getting close to her. Believe me, that shield is pretty strong. Btw when you say she doesnt do a lot of damage, thats a lie.

Likewise im just trying to point out that ap asssins are just no fun to play against, especially when they start to get kills. The only real weakness on them is late game (survive 45 min of bashing) or mr...which really puts a dent into your build.

I didnt say she can't do damage, she's just not very efficient. Fast is not efficient. The damage is split into different parts and no one part has much of the damage on it. Even then, if she delivers all of it oftentimes she has to do a bit of chasing for the kill. Did you notice that the orbs on her W can actually be dodged during her burst combo? Without the second jump she will possibly lose out on some defense. She has to be all in to do all her damage and tank maximum damage.

Rather than tanking fizz dodges and jukes. When he bursts you trying to get away is more or less pointless. Flash probably wont help you on its own. Right clicking isn't good enough.

Assassins don't really fall off lategame, they are just forced to play how they are meant to be played. They aren't supposed to be diving in and winning everything all day long. They clean up and they wreck close fights. They also displace key players, especially artilery champs like lux, kogmaw, and ezreal (ezreal isn't really one but he's often treated like one when he's being noncommital in team fights.).

When an assassin gets fed, you need to counterplay. You need to counterplay

When teamfights begin, tanks and fighters and anyone else who can disable and take damage are responsible for the safety of the others. In the world finals, a team made a huge mistake while eve was missing and they had commited all their tanky champs into a dive. They couldnt stop anything and they got messed up bad, the squishies were hunted down and murdered.

I'm pointing out that understanding the differences between champion types and why they get this and that explains alot including the question about ap assassins.

AD carries (Yi, Tryndamere, Ezreal, Caitlyn) aren't assassins.

Their kit lets them move around a lot. YES. THEY ARE ASSASSINS.
Ninjas. James Bond. It's called Skyfall, not Walk Through The Front Door.

AP assassins (LeBlanc, Kassadin) drop off late-game.
Early game advantage, late game drop. Pretty standard stuff.