The same notation is used for pointing at a single character or the first character of a null-terminated string:

char c = 'Z';
char a[] = "Hello world";

char *ptr1 = &c;
char *ptr2 = a;      // Points to the 'H' of "Hello world"
char *ptr3 = &a[0];  // Also points to the 'H' of "Hello world"
char *ptr4 = &a[6];  // Points to the 'w' of "world"
char *ptr5 = a + 6;  // Also points to the 'w' of "world"

The values in ptr2 and ptr3 are the same; so are the values in ptr4 and ptr5. If you're going to treat some data as a string, it is important to make sure it is null terminated, and that you know how much space there is for you to use. Many problems are caused by not understanding what space is available and not knowing whether the string was properly null terminated.

Note that all the pointers above can be dereferenced as if they were an array:

 *ptr1    == 'Z'
  ptr1[0] == 'Z'

 *ptr2    == 'H'
  ptr2[0] == 'H'
  ptr2[4] == 'o'

 *ptr4    == 'w'
  ptr4[0] == 'w'
  ptr4[4] == 'd'

  ptr5[0] ==   ptr3[6]
*(ptr5+0) == *(ptr3+6)

Late addition to question

What does char (*ptr)[N]; represent?

This is a more complex beastie altogether. It is a pointer to an array of N characters. The type is quite different; the way it is used is quite different; the size of the object pointed to is quite different.

char (*ptr)[12] = &a;

(*ptr)[0] == 'H'
(*ptr)[6] == 'w'

*(*ptr + 6) == 'w'

Note that ptr + 1 points to undefined territory, but points 'one array of 12 bytes' beyond the start of a. Given a slightly different scenario:

char b[3][12] = { "Hello world", "Farewell", "Au revoir" };

char (*pb)[12] = &b[0];

Now:

(*(pb+0))[0] == 'H'
(*(pb+1))[0] == 'F'
(*(pb+2))[5] == 'v'

You probably won't come across pointers to arrays except by accident for quite some time; I've used them a few times in the last 25 years, but so few that I can count the occasions on the fingers of one hand (and several of those have been answering questions on Stack Overflow). Beyond knowing that they exist, that they are the result of taking the address of an array, and that you probably didn't want it, you don't really need to know more about pointers to arrays.