$ find --version
find (GNU findutils) 4.10.0

The issue

The problem is present at least for these diagnostic messages but may be more global (I have not tested it further).

link-to-link loop:

$ ln -s link link
$ find -L -xtype l
find: ‘./link’: Too many levels of symbolic links
$

link-to-directory-to-link loop:

$ ln -s . link
$ find -L -xtype l
find: File system loop detected; ‘./link’ is part of the same file system loop as ‘.’.
$

directory with no permission:

$ mkdir dir
$ chmod 000 dir
$ find -type f
find: ‘./dir’: Permission denied
$

The message itself does not indicate if it is a warning message or an error message.

This has an impact on the user because:

• it indicates to the user:
  • where to find information on it
    • on GNU Findutils manual / 8.1.2 Warning Messages
    • on GNU Findutils manual / 12.1 Error Messages From find
  • therefore: if it can be silenced with -nowarn
• it enables to filter diagnostic messages by message type (with grep — see this example)

As a comparison, see the output (an extract) of the server Xorg:

Markers: (--) probed, (**) from config file, (==) default setting,
        (++) from command line, (!!) notice, (II) informational,
        (WW) warning, (EE) error, (NI) not implemented, (??) unknown.
(II) AIGLX: Suspending AIGLX clients for VT switch
(EE) client bug: timer event5 debounce: scheduled expiry is in the past (-54ms), your system is too slow

In the opposite, GNU Findutils manual / 12.1 Error Messages From find indicates that some error messages are prefixed by "Warning:", example: "Warning: filesystem /path/foo has recently been mounted".

PS

For users reading this report, the answer is that they are probably error messages (because not removed by the -nowarn option — or else they are warning messages and there is a bug in -nowarn):

link-to-link loop:

$ ln -s link link
$ find -L -nowarn -xtype l
find: ‘./link’: Too many levels of symbolic links
$

link-to-directory-to-link loop:

$ ln -s . link
$ find -L -nowarn -xtype l
find: File system loop detected; ‘./link’ is part of the same file system loop as ‘.’.
$

directory with no permission:

$ mkdir dir
$ chmod 000 dir
$ find -nowarn -type f
find: ‘./dir’: Permission denied
$