The technical difference between Composition and Aggregation in UML (and sometimes in programming too) is that with Composition, the lifetime of the objects composing the composite (e.g. an engine and a steering wheel in a car) is dependent on the composite object. While with Aggregation, the lifetime of the objects making up the composite is independent of the composite.

However I'm not sure about something related to composition in UML.

Say ClassA is composed of an object of ClassB:

class ClassA{
    ClassB bInstance;
    public ClassA(){
        bInstance = new ClassB();
    }
}

This is an example of composition, because bInstance is dependent on the lifetime of it's enclosing object.

However, regarding UML notation - I'm not sure if I would notate the relationship between ClassA and ClassB with a filled diamond (composition) or a white diamond (aggregation).

This is because while the lifetime of some ClassB instances is dependent of ClassA instances - there could be ClassB instances anywhere else in the program - not only within ClassA instances.

The question is: if ClassA objects are composed of ClassB objects - but other ClassB objects are free to be used anywhere else in the program: Should the relationship between ClassA and ClassB be notated as aggregation or as composition?