static - Declaration and Definition of variables in c

I understand the terms declaration and definition as below.

Declaration: This is just a heads up to the compiler that a variable of specified "name" and "type" exists in the code. So that it can be defined/assigned at later point of time

Definition: This is the process where an instance of the type is created by allocating a suitable space of memory.

int var; //Declaration and Definition-Agreed!!!
extern int var; //Declaration only ?
static int var; //Declaration only ?

My mind refuses to agree the second and third ones as declaration only statements. Because in many references I see, "extern and static variables are automatically initialized to zero upon memory allocation". And as you see in following code.

#include 
int main()
{

   static int i;
   printf("%d\n",i);
   return 0;
}

The output is 0. So Here it looks like the static int i; is declaration,definition and auto initialization statement. So please add your justification for this

Answer

Objects with static storage duration are initialized by zero in C.

static int a; // initialized by zero
int b;        // file-scope, static storage duration, initialized by zero

int main(void)
{
     int c;        // automatic storage duration, indeterminate value
     static int d; // initialized by zero
}

a, c and d are declarations and definitions of objects.

b is a declaration and a definition because there is no other file-scope occurrence of b until the end of the translation unit. Before the end of the translation unit, the declaration is a tentative definition.