How do `stat` and `file` differentiate symlinks?
The l in lrwxr-xr-x shows that is is a (symbolic) link.
Use readlink file to show where the symbolic link points to.

The stat manual page states:


  When invoked as readlink, only the target of the symbolic link is printed.  If the given argument is not a symbolic link, readlink will print nothing and exit with an error.