Problem Displaying Query Result

Question

I have been working through David's book 'Dreamweaver CS5 Training from the Source' and am attempting to adapt the tutorials for my own ideas.
My problem, I believe is in displaying the results of a database query. I want to display to the user a list of group names they are associated with.
The query looks like this:
$id = "$identity->user_id"; //logged in user
$sql = mysql_query("SELECT name
                               FROM groups
                               INNER JOIN user2group USING (group_id) // reference table contains user_id and group_id
                               WHERE user_id = $id
                               ORDER BY name")or trigger_error ( mysql_error ( ) );
while($row = mysql_fetch_array($sql)){
          $groups = $row['name'];
I attempt to display the results with:
<?php echo "$groups"; ?>
I have also tried:
$sql = mysql_query("SELECT name
                               FROM groups
                               INNER JOIN user2group USING (group_id) // reference table contains user_id and group_id
                               WHERE user_id = $id
                               ORDER BY name")or trigger_error ( mysql_error ( ) );
while($row = mysql_fetch_array($sql)){
          $groups = array();
          $groups[] = $row['name'];
and display with:
<?php echo implode('<br />', $groups); ?>
In both scenarios I get only one record displayed. (there is more than one record). The records seem to be available to display because if I change the ORDER command I get a different result.
Any help is much appreciated.
Thank you

Answer 1

Thank you so much for the explanation of the while loop it was extremely helpful. I was able to get my results to display correctly by including the echo statement in the while loop.
I spent several hours trying to use the array_push command with no success. I did explore the link you provided, but found many of the examples people gave to be very complicated. I would really like to start working with this command, if you would be able to provide me with an example based on my query and I can see it working I can start varying it to some of the more complicated methods given in the link.
Thank you again for your help.