In the original C standard the char type was not specified as signed or unsigned. This presented problems when char was used as a number.
Rather than change the behavior of char in existing implementations, the standards committee added two new types, signed char and unsigned char. So now there are three types of char.
So you should never use char as a numerical type, only unsigned char or signed char.
It is even possible that two compilers for a given machine will have different numerical behavior for char.
You can have three overloaded functions, f(char), f(signed char), and f(unsigned char).
For all other integer types there are two types, for example int is the same type as signed int. You can only have two overloaded functions with f(int) being the same as f(signed int).
Edit: I just remembered that with gcc you can have "char" signed or unsigned with flags -funsigned-char or -fsigned-char.