Running $apply on $rootScope vs any other scope

Another reason for running $apply on the $rootScope instead of $scope typically comes for me when I need to call $apply in a service which will be used by different controllers and therefore different scopes.
In this cases I prefer to inject the $rootScope to the service and call $apply on it without worrying on which scopes the service will be used in the future.

Running $apply on any scope always results in a $rootscope.$digest. The only case where it might make a difference is when you provide an expression as an argument to $apply. The expression will be evaluated in the current scope (vs. $rootScope), but afterwards $rootscope.$digest is always called.

The source code is quite clear: rootScope.js

Bottom line: If you call $apply with no arguments, it makes no difference.

Running $digest/$apply on any given scope will visit all other scopes using depth-first traversal:

https://github.com/angular/angular.js/blob/3967f5f7d6c8aa7b41a5352b12f457e2fbaa251a/src/ng/rootScope.js#L550-L558

That means that the only difference is that the $digest will start at whatever $scope it was called on