What are the differences between Abstract Factory and Factory design patterns?

I know there are many posts out there about the differences between these two patterns, but there are a few things that I cannot find.

From what I have been reading, I see that the factory method pattern allows you to define how to create a single concrete product but hiding the implementation from the client as they will see a generic product. My first question is about the abstract factory. Is its role to allow you to create families of concrete objects in (that can depend on what specific factory you use) rather than just a single concrete object? Does the abstract factory only return one very large object or many objects depending on what methods you call?

My final two questions are about a single quote that I cannot fully understand that I have seen in numerous places:

One difference between the two is that with the Abstract Factory pattern, a class delegates the responsibility of object instantiation to another object via composition whereas the Factory Method pattern uses inheritance and relies on a subclass to handle the desired object instantiation.

My understanding is that the factory method pattern has a Creator interface that will make the ConcreteCreator be in charge of knowing which ConcreteProduct to instantiate. Is this what it means by using inheritance to handle object instantiation?

Now with regards to that quote, how exactly does the Abstract Factory pattern delegate the responsibility of object instantiation to another object via composition? What does this mean? It looks like the Abstract Factory pattern also uses inheritance to do the construction process as well in my eyes, but then again I am still learning about these patterns.

Any help especially with the last question, would be greatly appreciated.

The Difference Between The Two

The main difference between a "factory method" and an "abstract factory" is that the factory method is a method, and an abstract factory is an object. I think a lot of people get these two terms confused, and start using them interchangeably. I remember that I had a hard time finding exactly what the difference was when I learnt them.

Because the factory method is just a method, it can be overridden in a subclass, hence the second half of your quote:

... the Factory Method pattern uses inheritance and relies on a subclass to handle the desired object instantiation.

The quote assumes that an object is calling its own factory method here. Therefore the only thing that could change the return value would be a subclass.

The abstract factory is an object that has multiple factory methods on it. Looking at the first half of your quote:

... with the Abstract Factory pattern, a class delegates the responsibility of object instantiation to another object via composition ...

What they're saying is that there is an object A, who wants to make a Foo object. Instead of making the Foo object itself (e.g., with a factory method), it's going to get a different object (the abstract factory) to create the Foo object.

Code Examples

To show you the difference, here is a factory method in use:

class A {
    public void doSomething() {
        Foo f = makeFoo();
        f.whatever();   
    }

    protected Foo makeFoo() {
        return new RegularFoo();
    }
}

class B extends A {
    protected Foo makeFoo() {
        //subclass is overriding the factory method 
        //to return something different
        return new SpecialFoo();
    }
}

And here is an abstract factory in use:

class A {
    private Factory factory;

    public A(Factory factory) {
        this.factory = factory;
    }

    public void doSomething() {
        //The concrete class of "f" depends on the concrete class
        //of the factory passed into the constructor. If you provide a
        //different factory, you get a different Foo object.
        Foo f = factory.makeFoo();
        f.whatever();
    }
}

interface Factory {
    Foo makeFoo();
    Bar makeBar();
    Aycufcn makeAmbiguousYetCommonlyUsedFakeClassName();
}

//need to make concrete factories that implement the "Factory" interface here