3-legged OAuth makes a roundtrip to the provider to obtain a token that represents the user. The user has to authenticate and grant access to the application.

2-legged OAuth has no roundtrip. It is simply a way to send a request that is signed with your consumer key and secret to identify your application to the service.

3-Legged using the Yahoo PHP SDK
<?php
require './Yahoo.inc';
require './oauth_secret.inc';

$session = YahooSession::requireSession($consumerKey, 
                                        $consumerSecret,
                                        $applicationId);  
$q = "select * from flickr.photos.recent";
$result = $session->client->query($q); 
print_r($result);
?>
3-Legged using the Yahoo PHP SDK
Array
( [query] => Array (
       [count] => 100
       [created] => 2008-09-12T02:22:21Z
       [lang] => en-US
       [updated] => 2008-09-12T02:22:21Z
       [uri] => http://query.pipes.yahoo.com/v1/yql?q=select+*+from+flickr.photos.recent
       [diagnostics] => Array (
          [url] => Array (
               [execution-time] => 555
               [content] => http://api.flickr.com/services/rest/?method=flickr.photos.getRecent
          )
          [user-time] => 575
          [service-time] => 555
          [build-version] => 2008.09.11.15:43
       )
       [results] => Array (
          [photo] => Array (
               [0] => Array (
                   [farm] => 4
                   [id] => 2851054416
                   [isfamily] => 0
                   [isfriend] => 0
                   [ispublic] => 1
                   [owner] => 29037411@N03
                   [secret] => 33955b4ee4
                   [server] => 3162
                   [title] => Uma corrente para organizar
               )
               ...