To figure out what is the difference between before_action and before_filter, we should understand the difference between action and filter.
An action is a method of a controller to which you can route to. For example, your user creation page might be routed to UsersController#new - new is the action in this route.
Filters run in respect to controller actions - before, after or around them. These methods can halt the action processing by redirecting or set up common data to every action in the controller.
Rails 4 –> _action
Rails 3 –> _filter