Service is a way to store persistent information over your application.
unlike the $scope, which is an new child of $rootScope per each route\controller.
The purpose of the Angular-specific implementation of already existent functions, is to make your life and work easier, by automatically telling angular to register your changes, and apply them to the current scope at the next $digest iteration.
I'll be happy to address any other questions.
Good luck with Angular! :)
I will now create an example plunk to emphasize the idea to you
UPDATE:
This is the plunker:
http://plnkr.co/edit/mVmhZpEdsZDQ0MUQpFJ7?p=preview
I used ng-change and the native change
keyup event to explain the point.
while using the angular built in ng-change directive requires no additional effort nor code, using the native events requires wrapping everything in the scope.$apply function/
calling scope.$digest manually.
(run the code and see for yourself)