Array is not a pointer. Your description of indexing is not correct, neither is the phrase "array pointer" you invented. The machine code produced will calculate the offset differently for a pointer and an array.
Let me clarify with an example. Suppose you have an array:
int a[10]
There is a section of memory of size
sizeof(int) * 10
somewhere, and the variable a is a
* int
that points to that section. When someone does this:
int x = a[2]
It is equivalent to:
int x = *(a+(sizeof(int)*2))
When I said "array pointer" in my previous comment, all it meant was the memory address that the variable (which is an array) points to (in the example, the variable "a")
a is a label, or an alias of a memory address. It is not a pointer. ( Your third example has a mistake, the correct increment is: a+2, because pointer arithmetic increments in object size not byte size )
Edit: missing paren