There’s no dedicated “character type” in C language. char is an integer type, same (in that regard) as int, short and other integer types. char just happens to be the smallest integer type. So, just like any other integer type, it can be signed or unsigned.
It is true that (as the name suggests) char is mostly intended to be used to represent characters. But characters in C are represented by their integer “codes”, so there’s nothing unusual in the fact that an integer type char is used to serve that purpose.
The only general difference between char and other integer types is that plain char is not synonymous with signed char, while with other integer types the signed modifier is optional/implied.