[fs.path.compare]

int compare(const path& p) const noexcept;

Returns:

(1.1)
Let rootNameComparison be the result of this->root_name().native().compare(p.root_name().native()).

If rootNameComparison is not 0, rootNameComparison.
(1.2)
Otherwise, if !this->has_root_directory() and p.has_root_directory(), a value less than 0.
(1.3)
Otherwise, if this->has_root_directory() and !p.has_root_directory(), a value greater than 0.
(1.4)
Otherwise, if native() for the elements of this->relative_path() are lexicographically less than native() for the elements of p.relative_path(), a value less than 0.
(1.5)
Otherwise, if native() for the elements of this->relative_path() are lexicographically greater than native() for the elements of p.relative_path(), a value greater than 0.
(1.6)
Otherwise, 0.

int compare(const string_type& s) const;
int compare(basic_string_view<value_type> s) const;
int compare(const value_type* s) const;

31 Input/output library [input.output]