Consider:
void foo1(char **p) { *p++; }
void foo2(char **p) { *p += 1; }
and
char *s = \"abcd\";
char *a = s;
foo1(&a)
The key is the precedence of the += and the ++ operator. The ++ has a higher precedence than the += (in fact, assignment operators have the second lowest precedence in C), so the operation
*p++
means dereference the pointer, then increment the pointer itself by 1 (as usually, according to the rules of pointer arithmetic, it's not necessarily one byte, but rather sizeof(*p) regarding the resulting address). On the other hand,
*p += 1
means increment the value pointed to by the pointer by one (and do nothing with the pointer itself).