AngularJS: controller vs service

Question

I have read a couple of posts regarding proper usage of angularjs entities: services, factories, controllers and directives.

My particular concern is a comparison of

Answer 1

controllers - responsibilities: initialize the view, mediate interaction between view/scope and services. It has dependencies on the view and model, but is more concerned with the view and making it work.

services - responsibilities: provides business services that is not dependent on the view or the controller. Its primary concern is delivering services, regardless of the consumer (controller/view/other services).

I'm not convinced if persistence factors into the differences.