The Nice Classification System categorizes products and services by class; you may file your trademark in one or more classes.
There are countries that allow one class per application, whilst others allow multiple classes within the same application.
The benefit of filing one application per class is that each class will have its independent process. If one class receives an objection or an opposition, the other applications/classes will not be affected. The disadvantage is that the price for various applications is higher.
Furthermore, filing a multi-class application (in the countries where this is possible) is cheaper, but there is a risk that the entire application is affected if one of the classes receives an objection or opposition.
In the first scenario, filing in more or less classes will not affect the registration probability each application. In the second scenario, if there are more classes, there is greater exposure and the chances of receiving objections or oppositions increase.
The Trademarks Office provides a certificate per application (not per class). Remember that not all countries allow a multi-class application.