Looks like a documentation problem. However I couldn't 
find this in documentation. Also the example output in 
mysqli_fetch_field returns 254. 
 
Could you please give me a link to the wrong 
documentation? 

Documentation isn't involved.  This is purely code.  The "type" property returned from the function != the value of the constant.

Perhaps your getting the right result is due to both of us running different versions of the software?  Here's what I'm on:

MySQL:  Ver 14.5 Distrib 4.1.2-alpha, for Win95/Win98 (i32)
PHP:    PHP 5.0.0-dev (cli) (built: Jun 28 2004 16:29:27)

Thank you for taking the time to write to us, but this is not
a bug. Please double-check the documentation available at
http://www.php.net/manual/ and the instructions on how to report
a bug at http://bugs.php.net/how-to-report.php

varchar column definition returns MYSQLI_TYPE_VAR_STRING, 
char column definition returns MYSQLI_TYPE_STRING. 

Ah.  Thanks for the clarification.  Then phpdoc/en/reference/mysqli/constants.xml needs updating.

You said:
varchar column definition returns MYSQLI_TYPE_VAR_STRING,
char column definition returns MYSQLI_TYPE_STRING.

Though the docs say:
MYSQLI_TYPE_STRING  (integer) 	Field is defined as VARCHAR
MYSQLI_TYPE_CHAR (integer) 	Field is defined as CHAR

BUT, not so fast...  CHAR columns return 253, but MYSQLI_TYPE_STRING's value is 254.  And MYSQLI_TYPE_CHAR is defined, but what's it for?

<?php
mysqli_query($db->connection,
             'CREATE TABLE bar (Vf VARCHAR(5),'
             . ' Cf CHAR(5))');

$r = mysqli_query($db->connection,
                  'SELECT Vf, Cf FROM bar');

$tmp = mysqli_fetch_field($r);
echo "$tmp->name type found = $tmp->type\n";
echo 'MYSQLI_TYPE_VAR_STRING = ' . MYSQLI_TYPE_VAR_STRING . "\n\n";

$tmp = mysqli_fetch_field($r);
echo "$tmp->name type found = $tmp->type\n";
echo 'MYSQLI_TYPE_STRING = ' . MYSQLI_TYPE_STRING . "\n\n";

echo "So, what's this for?...\n";
echo 'MYSQLI_TYPE_CHAR = ' . MYSQLI_TYPE_CHAR . "\n";

mysqli_query($db->connection,
             'DROP TABLE bar');
?>

vvvvvvv OUTPUT vvvvvvvvvvvv
Vf type found = 253
MYSQLI_TYPE_VAR_STRING = 253

Cf type found = 253
MYSQLI_TYPE_STRING = 254

So, what's this for?...
MYSQLI_TYPE_CHAR = 1
^^^^^^^^^^^^^^^^^^^^^^^^^^^

This bug has been fixed in CVS.

Snapshots of the sources are packaged every three hours; this change
will be in the next snapshot. You can grab the snapshot at
http://snaps.php.net/.
 
Thank you for the report, and for helping us make PHP better.

If anyone wonders about the second example returning 253/MYSQLI_TYPE_VAR_STRING for the CHAR column, it's due to silent column changes by MySQL:

"if a table contains any variable-length columns... all CHAR columns longer than three characters are changed to VARCHAR columns."

http://dev.mysql.com/doc/mysql/en/Silent_column_changes.html