If it exists, uint8_t must always have the same width as unsigned char. However, it need not be the same type; it may be a distinct extended integer type. It also need not have the same representation as unsigned char; for instance, the bits could be interpreted in the opposite order. This is a silly example, but it makes more sense for int8_t, where signed char might be ones complement or sign-magnitude while int8_t is required to be twos complement.
One further “advantage” of using a non-char extended integer type for uint8_t even on “normal” systems is C’s aliasing rules. Character types are allowed to alias anything, which prevents the compiler from heavily optimizing functions that use both character pointers and pointers to other types, unless the restrict keyword has been applied well. However, even if uint8_t has the exact same size and representation as unsigned char, if the implementation made it a distinct, non-character type, the aliasing rules would not apply to it, and the compiler could assume that objects of types uint8_t and int, for example, can never alias.