The difference between an abstract method and a virtual method

The stack is the memory set aside as scratch space for a thread of execution. When a function is called, a block is reserved on the top of the stack for local variables and some bookkeeping data. When that function returns, the block becomes unused and can be used the next time a function is called. The stack is always reserved in a LIFO (last in first out) order; the most recently reserved block is always the next block to be freed. This makes it really simple to keep track of the stack; freeing a block from the stack is nothing more than adjusting one pointer.

The heap is memory set aside for dynamic allocation. Unlike the stack, there's no enforced pattern to the allocation and deallocation of blocks from the heap; you can allocate a block at any time and free it at any time. This makes it much more complex to keep track of which parts of the heap are allocated or freed at any given time; there are many custom heap allocators available to tune heap performance for different usage patterns.

Each thread gets a stack, while there's typically only one heap for the application (although it isn't uncommon to have multiple heaps for different types of allocation).

To answer your questions directly:

To what extent are they controlled by the OS or language runtime?

The OS allocates the stack for each system-level thread when the thread is created. Typically the OS is called by the language runtime to allocate the heap for the application.

What is their scope?

The stack is attached to a thread, so when the thread exits the stack is reclaimed. The heap is typically allocated at application startup by the runtime, and is reclaimed when the application (technically process) exits.

What determines the size of each of them?

The size of the stack is set when a thread is created. The size of the heap is set on application startup, but can grow as space is needed (the allocator requests more memory from the operating system).

What makes one faster?

The stack is faster because the access pattern makes it trivial to allocate and deallocate memory from it (a pointer/integer is simply incremented or decremented), while the heap has much more complex bookkeeping involved in an allocation or deallocation. Also, each byte in the stack tends to be reused very frequently which means it tends to be mapped to the processor's cache, making it very fast. Another performance hit for the heap is that the heap, being mostly a global resource, typically has to be multi-threading safe, i.e. each allocation and deallocation needs to be - typically - synchronized with "all" other heap accesses in the program.

A clear demonstration:
_{Image source: vikashazrati.wordpress.com}

Maybe a bit of example code will help: Notice the difference in the call signatures of foo, class_foo and static_foo:

class A(object):
    def foo(self, x):
        print(f"executing foo({self}, {x})")

    @classmethod
    def class_foo(cls, x):
        print(f"executing class_foo({cls}, {x})")

    @staticmethod
    def static_foo(x):
        print(f"executing static_foo({x})")

a = A()

Below is the usual way an object instance calls a method. The object instance, a, is implicitly passed as the first argument.

a.foo(1)
# executing foo(<__main__.A object at 0xb7dbef0c>, 1)

With classmethods, the class of the object instance is implicitly passed as the first argument instead of self.

a.class_foo(1)
# executing class_foo(<class '__main__.A'>, 1)

You can also call class_foo using the class. In fact, if you define something to be a classmethod, it is probably because you intend to call it from the class rather than from a class instance. A.foo(1) would have raised a TypeError, but A.class_foo(1) works just fine:

A.class_foo(1)
# executing class_foo(<class '__main__.A'>, 1)

One use people have found for class methods is to create inheritable alternative constructors.

With staticmethods, neither self (the object instance) nor cls (the class) is implicitly passed as the first argument. They behave like plain functions except that you can call them from an instance or the class:

a.static_foo(1)
# executing static_foo(1)

A.static_foo('hi')
# executing static_foo(hi)

Staticmethods are used to group functions which have some logical connection with a class to the class.

foo is just a function, but when you call a.foo you don't just get the function, you get a "partially applied" version of the function with the object instance a bound as the first argument to the function. foo expects 2 arguments, while a.foo only expects 1 argument.

a is bound to foo. That is what is meant by the term "bound" below:

print(a.foo)
# <bound method A.foo of <__main__.A object at 0xb7d52f0c>>

With a.class_foo, a is not bound to class_foo, rather the class A is bound to class_foo.

print(a.class_foo)
# <bound method type.class_foo of <class '__main__.A'>>

Here, with a staticmethod, even though it is a method, a.static_foo just returns a good 'ole function with no arguments bound. static_foo expects 1 argument, and a.static_foo expects 1 argument too.

print(a.static_foo)
# <function static_foo at 0xb7d479cc>

And of course the same thing happens when you call static_foo with the class A instead.

print(A.static_foo)
# <function static_foo at 0xb7d479cc>