So are Garen and Shyvana tanks?

juggernauts. They don't die but they'll kill your team

no, they're fighters

they just build very tanky because they don't have a lot of mobility and their base damage is really high

it dont matter

They are Juggernauts, which are a subclass of Fighters. They are not Tanks.

Everyone calls them tanks because you build tanky, technically there not because none of their abilites increase their tanky-ness but meh there both tanks lol

they are tanky, good as a damage sponge, but the "real" tanks have more cc than them. shyvana also has no real tanky steroid i.e. nothing in her kit makes her more tanky except for her weak passive, well and bonus health on her ult, still not enough

if your team is squishy it's better to pick shyvana than kindred, for instance

arguing about the exact role names is a silliness, like i don't see much difference between hecarim and amumu but some people do...

No, they are both Fighters who can get Tanky.

Garen was once a tank.

Now he's more of a fighter/diver with some defensive prowess.

They both live longer than half the tanks but lack hard c/c

In the most not-silly sense no they are absolutely positively not tanks.

But some people do call them tanks anyways.

The term now used for them is "juggernaut"