From what I have read, batteries provide an electrochemical potential that causes electrons to move from the negative terminal through a conductor to the positive terminal.
I have read numerous explanations for why this happens. Many of these explanations include voltage, electric field, and emf. However, I have seen many stating that batteries are not coulombic devices--that the negative/positive terminal isn't negatively/positively charged.
If charge plays no part in a battery's operation, then exactly what force makes the electrons move? The only way that this makes sense to me is if they simply diffuse to the positive terminal because of the difference in concentration (and even this is a charge imbalance).
Link explaining that batteries are not electrostatic devices: