Even when they say that all services and factories are singleton, I don't agree 100 percent with that. I would say that factories are not singletons and this is the point of my answer. I would really think about the name that defines every component(Service/Factory), I mean:
A factory because is not a singleton, you can create as many as you want when you inject, so it works like a factory of objects. You can create a factory of an entity of your domain and work more comfortably with this objects which could be like an object of your model. When you retrieve several objects you can map them in this objects and it can act kind of another layer between the DDBB and the AngularJs model.You can add methods to the objects so you oriented to objects a little bit more your AngularJs App.
Meanwhile a service is a singleton, so we can only create 1 of a kind, maybe not create but we have only 1 instance when we inject in a controller, so a service provides more like a common service(rest calls,functionality.. ) to the controllers.
Conceptually you can think like services provide a service, factories can create multiple instances(objects) of a class