const char*  vs char* const

In C,

In the code below, I just want to be 100% sure that I understand the difference between statements (A) and (B):

void try_this(char *p, char *q)
{
       const char*  constptr = p;  // (A)
       char* const constptr2 = p; // (B)
}


(A) means that the data being pointed TO is constant
(B) means that the POINTER (address) is constant.

Now assuming that's the case, I could use some clarification on (A):
Suppose p was passed into the above function as "HELLO"
Suppose q was passed into the above function as "GOODBYE"

constptr  points to the beginning of "HELLO".
I cannot say *constptr = 'J' because of the nature  of the const.

But I can say
constptr = q;  // now it will point to "GOODBYE"
(is this legal???.....)

Thanks
Steve
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