You didn't read the post I linked, did you? These classes are from Riot, not me.
Here, I'll explain it in detail.
Slayers are split into:
Assassins - These are melee or otherwise short-ranged champions who have to get into the fray at risk of collapsing from the enemy's damage, but make up for it in ridiculous burst damage and defensive tools. Most commonly, the defensive tools take the form of rapid mobility, with the Assassin dashing, leaping, or blinking back and forth across the battlefield in the blink of an eye. Their damage and mobility is offset by their lack of defensive stats, often having low armor values and health pools. 
Skirmishers - These slayers typically stay in the middle of the fight for a sustained period of time and shred through every opponent at least once. They don't have typically high burst damage, but they have many defensive tools that can allow them to remain in the midst of the fight, ranging from simple stat boosts and healing effects to mechanics that need to be utilized cleverly, like projectile blocking barriers and attack nullifying parries, along with deadly sustained damage. 
Fighters are split into:
Juggernauts - Juggernauts are titanic fighters who are meant to both dish out and soak up massive amounts of damage in exchange for their viable combat strategies generally being limited to "run at the enemy and kill them when you reach them". Strong, and among the largest characters physically, they're offset by their lack of mobility and outplay potential, requiring enemies to be within their radius. This leaves them susceptible to kiting, but if they reach you, death is imminent. Their overwhelming damage can be as quick and brutal as an Assassin's.
Divers - Also known erroneously by fans as "bruisers," Divers are the typical balance between damage and tankiness, something of a midway between Juggernauts and Skirmishers. Divers are so named because, often, they have a single ability that allows them to "dive", or cover a large distance in a burst of mobility. This doesn't rival the fluid motions of an Assassin or rapid dances of a Skirmisher, but it's enough for them vault over a fight to vulnerable enemies behind. Once there, they just smack enemies until they die. 
Tanks are split into:
Vanguards - More offense-based tanks, vanguards are more encouraged to lead their team by starting fights using explosive initiation, mostly to catch enemies making positioning mistakes and punishing them heavily with crowd control, and hopefully if a sufficient damage-dealing ally is with them, death. These tanks, often, can bleed into Juggernaut territory, depending on the item build. 
Wardens - More defense-based tanks, Wardens draw a line in the sand and prevent enemies from crossing. While they lack a Vanguard's raw initiation prowess, they make up for it with even more overwhelming crowd control, often being host to multiple slow, stun, and root effects. By sticking close to squishy allies, a Warden prevents a sneaky Assassin or daring Diver from destroying their vulnerable companion. 
I won't list the others, since they aren't relevant.
Warwick, according to Riot, falls under the Diver category.
