Different roles

I've been teaching a bunch of new friends to play League over the years, and when I've explained all the roles, I've come to think of the exact definitions of them all.

The roles I usually think of is:

TANKS Their purpose is to soak damage so the rest of the team don't have to, and to be able to engage a teamfight and therefore most commonly have at least some kind of cc. I'm thinking about guys like Amumu or Malphite.

FIGhTERS Their job is to fight for sustained periods of time and are overall auto attack-based and therefore not dependent on cooldowns so much. They excel in 1v1 fights but are often dependent on their team for larger fights cause they are sensitive to cc. Examples are Xin Xiao and Olaf

CARRIES Reason for birth: damage! Overall weak in the beginning of a game but grows powerful in the end. Overall extremely sensitive to cc cause of low mobility and glassy builds, since their sole purpose is to deal huge amounts of damage, generally at range. Examples Ashe and Annie

ASSASSINS Blowing other high-value squishy champions(usually carries) up in a second and then disappears into thin air (kinda). A little bit like Carries since they deal extreme damage and die easily, but with the biggest difference usually being melee ranged, high mobility and ability to escape from a successful assassination. Example Akali and Zed

SUPPORTS Helps the rest of the team by healing, speeding them up, slowing enemies down, shielding allies and things like that. Are most often squishy and have low damage. They are bad 1v1 and bad at fighting overall, but make up for it by being good at protecting the team, disrupting and disabling the enemy for the rest of the team to kill.

Then I've started thinking of it as 3 kinds of baseroles split into 2 or 3 versions.

The 3 baseroles is:

SUPPORTS Split into tanks and "ordinary" supports. Where you can see them as the "front" kind of supports(Ex. Leona and Alistair) and the "behind" kinds, standing behind or at least beside the carries(Ex. Janna and Lulu). The tanks are the ones soaking damage and doing engages, and the normal supports are most often ranged, squishy and poke, heal, shield and cc. So ye, simply the more utility-based supports of the two.

CARRIES Split up into marksman(adc) and mage(apc), where the main difference ofcource is their damagetypes being AD and AP, but also that the marksman are sustain-carries and the mages are burst-carries.

FIGHTERS Split into bruisers who jump in on enemies to cc them, juggernauts who chase down enemies and assassins who jump in and blow people up in an instant :P Ofcource Assassins could be, and are often referred to as, it's own category, but I'm thinking they might be a part of the base-category "fighter".

The reason I'm making this post is cause I am asking myself how wrong I am :P And because I'm curious about what the official definitions is, if there are any. Cause for example, what is a bruiser according to you guys? I've heard several...