As the documentation itself mentions $digest cycle is peformed any time you do $scope.$apply. As per developer guide on scope
After evaluating the expression, the $apply method performs a $digest.
In the $digest phase the scope examines all of the $watch expressions
and compares them with the previous value.
Usually you don't call $digest() directly in controllers or in
directives. Instead a call to $apply() (typically from within a
directives) will force a $digest().
So you should not explicitly call $digest, you calling $apply method would trigger a digest cycle.
scope.$digest() will fire watchers on the current scope, and on all of its children, too. scope.$apply will evaluate passed function and run $rootScope.$digest().
The first one is faster, as it needs to evaluate watchers for current scope and its children. The second one is slower, as it needs to evaluate watchers for$rootScope and all it's child scopes.
When an error occurs in one of the watchers and you use scope.$digest, it's not handled via $exceptionHandler service, so you need to handle exception yourself. scope.$apply uses a try-catch block internally and passes all exceptions to $exceptionHandler.