PSA: Divers and Assassins are two completely different classes
I see alot of people throwing the term Assassin around but using it to define completely Diver related champions and concepts. It seems that the majority envisions an Assassin to simply be someone that deletes a single target.
Assassins however are not the only class defined by single target deletion. You also have Divers whose role is to target a single enemy and Dive past resistance using tankiness, some form of CC immunity and some form of single target CC lockdown to completely obliterate it. Following this, Divers then proceed to brawl in the midst of the enemy team. Divers also just so happen to be some of the best gankers in the game since they specialize in single target lockdown and deletion. Just look at 
.
An Assassin's role however is to wait until they see an opening where CC/damage won't keep them from their target and use their gap closing tools to catch it and delete it with a full spell rotation before using an escape tool to get out and look for another opening. Assassins do not want to charge head on and they don't want to stick around in the midst of 4 enemies after deleting a target as that's basically suicide.
Divers and Assassins tend to dip into each others skillsets sometimes just like any other archtype does (such as Ahri being a pseudo-Assassin) but it's fairly simple to see what their true identity is (such as Ahri is still a Burst Mage).
So onto a more recent misuse of the term Assassin lets look at Rengar and the things he has that Assassins don't have and Divers do.
- Great ganking potential due to single target lockdown and deletion capabilities.
- The ability to continue brawling in the midst of the enemy after killing his target.
- The ability to dive past resistance tactically using stealth and the ability to either lock his target down with E or ignore incoming CC and some damage with W.
Now let's look at the traits that align him with the Assassin archtype.
- He can escape after a kill with empowered W (maybe) and Stormraider if he's running it.
- Can't literally dive head on as he has to keep his distance during his ult to remain unseen.
Not much huh? And even then what's there is pushing it.
So when you all say that you want Rengar to be an Assassin are you saying you want his plethora of Diver tools removed in exchange for proper Assassin escape tools or are you just misusing the term "Assassin" when what you really mean to say is "reliable burst"?
, who are classified as Divers but often played like Assassins.
vs 
vs 
, your goals vary just a bit, but you're still utilizing the kit in generally similar ways. As a clarification, even tank is no longer a class, because there are different ways of doing it. Now, instead, we have
wardens (
) who disrupt as they tank, and juggernauts (
) who lack CC while they tank (with generally low mobility compared to divers and assassins). The champion damage and tankiness is generally not part of a class, simply because it's easy to build out of those subclasses. However, kit-based classes are more commonly accurate, as kits are designed to scale in that direction.
for free, and 
) defend and Vanguards(
) initiate.
. Her CC is just too limited, and she builds strong enough to pick off a squishy moreso than protecting people. Naut meanwhile has CC all over the place, but limited mobility in and no reliable ranged CC, so he's better off peeling until he can find that sweet hook spot, if he can afford to hold that. Sometimes you can ult them down, but most carries can outrun that thing a very long distance, if they even feel threatened by your rooting abilities alone.
feels like a Warden/Juggernaut. When your initiation is running up to people and using your short-ranged ult on one target, you're not a damn Vanguard, much less a Diver. Low mobility, high tankiness, good damage (although typically more AoE than single target)? That says Juggernaut. Two medium-short ranged hard CCs, one of which is an absolute boatload of "get off my carry" says Warden.
= [galio-happy]
= [garen-swing]
= [fiora-cool]
is a diver, and not an assassin? Her escape tools are basically nil (W is less an escape and more a breather, R requires an enemy target), and her common builds almost support a diver playstyle. Yet, at the same time, she's squishy as hell, and typically instakilled by CC.