__class__ is a data descriptor object. Many attributes on Python core objects are implemented as descriptors. You should see that as an implementation detail, nothing more.
__class__ is a descriptor because Python needs to be able to validate new values you assign to it; there are certain limitations to assigning to __class__ that need to be honoured, and making __class__ a descriptor is the most efficient method of doing so.
Descriptor objects are automatically found and invoked on the type when you try to access the attribute on an object. instance.__class__ will find and execute the __class__ descriptor on the class (by searching through all classes in the inheritance graph), typically ending up with object.__dict__['__class__'].__get__(instance, type(instance)) (where object is usually the first class on which the __class__ attribute is found in the type(instance).__mro__ sequence); This happens because Python will always use the type's __getattribute__ method to find attributes, and that method knows how to handle descriptors found on the class and bases, as well as look at the object.__dict__ attributes. So they don't live on the object __dict__ itself, they live on the object type, by design.
Now, class objects are also callable objects. That's how you create an instance; for a given class Foo, you create an instance by calling it, so Foo(). instance.__class__ is just a reference to the class object, just like class_obj = Foo would create a reference to a class. Calling the class object produces a new instance, whatever reference you used to get to it.
Finally, type.__class__ is just a reference to type() itself:
>>> type.__class__ is type
True
>>> type.__class__
<class 'type'>
>>> type(type)
<class 'type'>
That's because type is its own type. The parent-child relationships of the Python type system must stop somewhere, and type is that point.
In your example, a.__class__ is a reference to the Foo class. And type.__class__ is the same object as type, so you essentially did this:
Foo == type(a)
which is indeed true, the type of a is Foo.