Difference between bruiser, juggernaut and tank

Bruiser no longer exists. The classes are:

Skirmisher -
High damage and mobility, generally not good at team fights but great at dueling

Diver - Less damage than skirmisher with stronger engage for team fight but usually not a way to escape after engaging

Juggernaut - High damage, health, and sustain but almost no mobility outside of movement speed so they are prone to being kited but will win against almost anyone when they are in range

Tank - Multiple CC skills with either defense built into their kit or deal damage based on defensive stats

Bruiser is a superclass that contains juggernauts and divers, much like "slayer" is a superclass that contains skirmishers and assassins.

Juggernauts are tanky, high damage champions who have low to no mobility and generally have low to moderate CC. Darius, Garen, Nasus, Illaoi, Mundo, and Mordekaiser are all in this class. There's also argument that Singed might be a juggernaut, but I don't think anyone's actually decided on that one. Their biggest weakness tends to be being kited, since they can't do much of anything to someone they can't catch

Tanks are generally tankier than juggernauts and tend to have moderate to high CC, low to moderate damage, and sometimes have utility. They're split into two subclasses - Wardens and Vanguards.

Wardens are like Braum and Tahm Kench - They're meant to keep their allies alive. They generally have poor engage and low damage, but have additional utility to help save allies. Generally they tend to be tankier than Vanguards.

Vanguards are like Leona and Malphite - They're meant to go in and lock enemies down and keep them from doing much of anything. They generally have higher engage and mobility than Wardens, but tend to have less utility to compensate. Usually they're a bit more fragile than Wardens, but they're still almost always tankier than juggernauts.

Divers are the jacks of all trades in League. They're durable, but not really tanky, they have both burst and DPS, but not as much burst as assassins or DPS as ADCs, and they have engage and CC, although less of each than tanks. They also tend to lack any ability to escape that isn't just "run like hell" or "murder everyone". They do a lot, but not as well as actual specialists - an 0/2 J4 isn't really a threat to an ADC, but an 0/2 Zed is still very much a threat. They tend to either build like juggernauts or like assassins depending on the champion and the patch. Examples are J4, Wukong, Lee Sin, Diana, and Vi.

Skirmishers aren't in your list, but they're similar to Divers and tend to be confused with them. Skirmishers are squishy, high DPS melee champions, and tend to have a strong defensive ability or two. The easiest way to think of them is as melee ADCs, honestly. They sometimes have a bit of burst, but they're generally still DPS-oriented. Generally they tend to scale well into late, although not always, and they tend to attract the most circlejerks about them. The difference between them and divers isn't always clear, but as a general rule skirmishers tend to be squishier, have worse engage, and have to rely on their defensive ability (or abilities) to actually survive. Why are they under the same superclass as assassins? I have no fucking clue. Examples are Yasuo, Fiora, Yi, and Tryndamere.

You can think of them in terms of power. The higher the power, the less room they have for other stuff like utility & movement abilities. Juggernauts would be the strongest and only have a tiny amount of utility and often zero mobility. Off the top of my head, the only mobile juggernaut is Garen and none of them have stuns or roots except for Urgot?

Then the next would be bruisers. Their strength isn't as high as Juggernauts, so they get to enjoy more utility and mobility. Pretty much every one of them has a dash and a good number of them have a stun or displacement ability.

Last would be tanks. Lowest strength(generally so, some have an abusive amount of base dmg), highest utility. Every single one of these champions have multiple abilities with CC. Their mobility isn't much worth noting, but, generally speaking, they're still more mobile than Juggernauts.