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
Stack allocation is much faster since all it really does is move the stack pointer.
Using memory pools, you can get comparable performance out of heap allocation, but that comes with a slight added complexity and its own headaches.
Also, stack vs. heap is not only a performance consideration; it also tells you a lot about the expected lifetime of objects.
Best Answer
LR is link register used to hold the return address for a function call.
SP is stack pointer. The stack is generally used to hold "automatic" variables and context/parameters across function calls. Conceptually you can think of the "stack" as a place where you "pile" your data. You keep "stacking" one piece of data over the other and the stack pointer tells you how "high" your "stack" of data is. You can remove data from the "top" of the "stack" and make it shorter.
From the ARM architecture reference:
This link gives an example of a trivial subroutine.
Here is an example of how registers are saved on the stack prior to a call and then popped back to restore their content.