Banks are in the service industry (as is just about everything else; only resource extraction and manufacturing are excluded), so not just "more of". It is definitively a service industry position.
> like being a cashier.
The physical action of the work is a lot like being a cashier, but the environment in which the work is done is usually different, and that environment (especially with respect to the type of clothing the people usually wear within that environment) is what traditionally defines "white collar". As such, tellers are considered white collar by most people.