Yes and no, AP champions have their categories as much as their AD counterparts.
Battlemages do tons of damage during a protracted teamfight, a could use items that amplify their ability to either slowly kill the frontline or to deal consistent amounts of aoe to the whole enemy team.
Burst mages can create zones of threat, a can 100-0 a squishy target with ease. They can't get past the frontline though, so they could either use items that make them somewhat dangerous to tanks/bruiser (doesn't mean the should be able to oneshot tanks, of course), or items that help them attack the backline with the proper positioning. Also they tend to have some form of CC, that makes them still useful even if they're waiting for their damaging abilities to recharge. But it's better for them to focus on the burst, rather than becoming CC machines.
AP assassins tend to have more AoE and/or CC than AD assassins, while still having the access to the backline that ad assassins have, and burst mages don't. Katarina has the AoE of burst mages and the mobility of assassins, but lacks the CC that pretty much every burst mage has, while Fizz has some CC and initiation, at cost of some AoE damage (he still destroys single targets). Akali's kit has aged really well so I won't talk about her :P.
And these are just the main categories, that where introduced by riot. If you want you can differentiate mages even further. Heck, Karthus single target Q and Anivia empowered E count as crits, and that's intended, so much that their damage is reduced by randuin. Instead of fixing that, I'd say they should delve deeper into the idea of mages with the ability to crit (of course with the proper items, not with infinity, shiv and such).
Azir and cassio are considered as some sort of AP carries, why not expand on that?
Cho is an AP juggernaut, problem is, there's no AP item that properly shreds MR, which means that even his E at high levels doesn't help that much, and he only relies on his R, which is a tad too strong right now. Give him an item that shreds MR and maybe he won't need that much true damage.
But if you're talking specifically about the items AP champs currently have, you're totally right.