Scope is a special JavaScript object which plays the role of joining controller with the views. Scope contains the model data. In controllers, model data is accessed via $scope object. $rootScope is the parent of all of the scope variables.

Using service method, we define a service and then assign method to it. We've also injected an already available service to it.
mainApp.service('CalcService', function(MathService){
   this.square = function(a) { 
      return MathService.multiply(a,a); 
	}
});

Services are JavaScript functions and are responsible to do specific tasks only. Each service is responsible for a specific task for example, $http is used to make ajax call to get the server data. $route is used to define the routing information and so on. Inbuilt services are always prefixed with $ symbol.

Using factory method, we first define a factory and then assign method to it.
var mainApp = angular.module("mainApp", []);
mainApp.factory('MathService', function() {     
   var factory = {};  
		
   factory.multiply = function(a, b) {
      return a * b 
   }
   return factory;
});

factory method is used to define a factory which can later be used to create services as and when required whereas service method is used to create a service whose purpose is to do some defined task.