A char array is just that - an array of characters:
A string is a class that contains a char array, but automatically manages it for you. Most string implementations have a built-in array of 16 characters (so short strings don't fragment the heap) and use the heap for longer strings.
You can access a string's char array like this:
std::string myString = "Hello World";
const char *myStringChars = myString.c_str();
C++ strings can contain embedded \0 characters, know their length without counting, are faster than heap-allocated char arrays for short texts and protect you from buffer overruns. Plus they're more readable and easier to use.
However, C++ strings are not (very) suitable for usage across DLL boundaries, because this would require any user of such a DLL function to make sure he's using the exact same compiler and C++ runtime implementation, lest he risk his string class behaving differently.
Normally, a string class would also release its heap memory on the calling heap, so it will only be able to free memory again if you're using a shared (.dll or .so) version of the runtime.
In short: use C++ strings in all your internal functions and methods. If you ever write a .dll or .so, use C strings in your public (dll/so-exposed) functions.