The difference between static and instantiated methods and properties seem to be one of the biggest obstacles to those just starting out with OOP PHP in PHP 5.
The double colon operator (which is called the Paamayim Nekudotayim from Hebrew - trivia) is used when calling an object or property from a static context. This means an instance of the object has not been created yet.
The arrow operator, conversely, calls methods or properties that from a reference of an instance of the object.
Static methods can be especially useful in object models that are linked to a database for create and delete methods, since you can set the return value to the inserted table id and then use the constructor to instantiate the object by the row id.