Here is my perspective:
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Assassin: delete 1 or 2 people, try to survive
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Skirmisher: 2v2s, 2v3s, 3v3s
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Duelists: 1v1s, 1v2s (win lane, win game)
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Hypercarry: Champions that offer almost nothing but tons of damage for their team in a teamfight
I would consider Yasuo a Hypercarry, but he's also a Slayer. Slayer being basically Melee ADC such as Tryndamere, Fiora, or Yasuo. Tryndamere and Fiora on the other hand are duelists in my eyes.
Other categories of champs that can be Hypercarrys are Marksman (Draven, Kog'maw), certain mages (Viktor, Azir), certain assassins (old Akali, old Katarina. I don't know if this will change in the rework), hopefully you get the idea.
Yasuo isn't suited for 2v2s, 2v3s, etc. Champions that I would consider prime examples of skirmishers would be Lee Sin, Elise, Ekko, and Fizz. All of these champions have above average CC (Yasuo's CC is relatively situational), unrestricted mobility (Yasuo relies more on minions, skirmishers don't always fight in lanes), you get the idea. Yasuo doesn't really fit in with the other champions I listed.
Also notice how almost all skirmishers are played/can be played in the jungle, with a few exceptions such as Ahri or Kassadin. Yasuo can clear the jungle relatively well, but he lacks immediate pressure and requires stacking his Q and being by a ton of minions (aka best in lane). Kassadin and Ahri on the other hand don't jungle because I imagine their clear's are horrendous.