First: STOP THINKING ABOUT GLOBAL VARIABLES IN C AND C++, or you will perpetuate your state of confusion. The issue is more complex than in, e.g., Python or Pascal, and therefore you can't just use a single word for the concept(s).
Second, there is no "heap" or "stack" -- these are operating system and CPU details, and have nothing to do with the abstract C++ language specification.
Now, variables have 1) scope, 2) linkage and 3) storage class. The static keyword is used to affect the all three aspects, depending on where you use it.
Scope: where the variable is declared. If within a function, it is a function-scope, if outside of a function, it is file-scope (what you probably refer to as "global variable").
Linkage: whether the variable is accessible from other compilation units (relevant when your program consists of multiple source files).
Storage class:
Static variables are allocated in implementation-defined manner upon program startup, and they live until the program ends. They cannot be "freed" or "reallocated". (a typical implementation are BSS and DATA segments as others have mentioned).
Automatic variables exist only at function scope, they are allocated (and possibly initialized) on function entry (usually on the CPU's stack) and deallocated on function exit.
Dynamic storage class is what you probably refer to "the heap". Those are variables whose storage is directly manipulated through malloc/free or new/delete. Storage for static variables is managed in a VERY different way than dynamic storage, and the two kinds of storage are fundamentally incompatible.
Example:
===
// ALL file-scope variables have static storage class
int global1; // file-scope, external linkage
static int global2; // file-scope, internal linkage
void f()
{
static int x; // static storage class, function-scope
int y; // automatic storage class, function-scope
free(&x); // ILLEGAL, WILL CRASH!
free(&y); // DITTO!
free(&global1); // DITTO!
}
===
Now, all variables with static storage class (global1, global2 and x) are allocated and initialized before program startup. If you do not specify initial values, they are default-initialized in UNSPECIFIED ORDER. (For primitive types, this just means filling with zeros).
Static variables are deallocated only at program exit. This means, that 'x' in function f will be initialized ONLY ONCE (at program startup) and that it will RETAIN ITS VALUE between invocations of the function (as opposed to y which will be allocated on each function entry and deallocated at each function exit, thus also its value destroyed). Note that using static variables within functions is very incompatible with multithreading and reentrancy, unles you know very well what you're doing.