I suppose I should mention that the "char" datatype only holds a single character. To hold more than one, you'd need an array of chars. Of course that brings up the issues of array length, and how arrays are treated (nearly) identically as pointers.
The array length is a memory allocation issue. Either set a fixed static size that is guaranteed to be big enough, or use dynamic memory allocation, which requires explicit new/delete (or malloc/free) calls, which can be expensive if called frequently.
The pointer issue is important when doing comparisons. If you wrote the code you have above, it would compare the pointers to each other. That is, it would compare the addresses of two strings in memory, rather than the contents of the two strings. Hence two strings with identical characters would compare differently because they are stored in different memory locations. You'd need to use a string comparison function, such as strncmp (or strcmp, if you don't know a max length, and there is no possibility of missing null terminators).
There are a number of string classes in C++ that basically wrap char arrays to handle the details for you, such as the CString class. I usually just end up using raw char arrays though, but then I don't usually do anything fancy with strings.