Is riven an assasin or a fighter?

She's a fighter, not an assassin. She never has been, never will be.

Don't worry about classifications. She's a primary fighter secondary assassin, but she can be built either way.

Primary Role: Fighter Secondary Role: Assassin

Both

I don't think she is neither...she is a caster. She is more close to being an AD mage than anything else.

To be considered fighter you have to rely on aa once you burned your abilities. Riven CDs are so low that she rarely stumbles onto this scenario, and even if you burn everything at once your aa would be empowered at that point thanks to your passive.

To be considered assassin you need to be able to jump into the back line somehow and then due a high burst before working your way back. Eventhough riven mobility is high, is not the type of mobility that would allow her to go into the back lines (unless she is fed enough to mow down all the front line) her mobility is based on short continuous dashes. and not one big dash that allows her to go directly into the back line.