update and updatecode commands missing?

I would like to be able to update my modules using drush. I read in another issue that the "pm update" commands are gone and replace by update and updatecode (which doesn't run update.php?) These commands don't seem to be available on my install.

When I run drush help, I get the following:

Execute a drush command. Run `drush help [command]` to view command-specific
help.

Examples:
  drush dl cck zen                     	Download CCK module and Zen theme.                 
  drush --uri=http://example.com status	Show status command for the example.com multi-site.

Options:
  -r <path>, --root=<path>	Drupal root directory to use (default: current directory)            
  -l <uri> , --uri=<uri>  	URI of the drupal site to use (only needed in multisite environments)
  -v, --verbose           	Display all available output                                         
  -q, --quiet             	Hide all output                                                      
  -y, --yes               	Assume 'yes' as answer to all prompts                                
  -s, --simulate          	Simulate all relevant actions (don't actually change the system)     
  -i, --include           	A list of paths to search for drush commands                         
  -c, --config            	Specify a config file to use. See example.drushrc.php                
  -u, --user              	Specify a user to login with. May be a name or a number.             
  -b, --backend           	Hide all output and return structured data (internal use only).      

Commands: 
  dl                  	Download core Drupal and projects like CCK, Zen, etc.                                             
  help                	Print this help message. Use --filter to limit command list to one command file (e.g. --filter=pm)
  status              	Provides a birds-eye view of the current Drupal installation, if any.                             
  updatedb            	Execute the update.php process from the command line
  sql conf            	Print database connection details.                             
  sql version server  	Print database server version number.                          
  sql version client  	Print database client library version number.                  
  sql dump            	Exports the Drupal DB as SQL using mysqldump.                  
  sql query           	Execute a query against the site database.                     
  sql load            	Copy source database to target database.                       
  sql cli             	Open a SQL command-line interface using Drupal’s credentials.
SQLSTATE[HY000] [2002] Can't connect to local MySQL server through socket '/var/lib/mysql/mysql.sock' (2)                       [warning]

When I run drush help updatecode:

SQLSTATE[HY000] [2002] Can't connect to local MySQL server through socket '/var/lib/mysql/mysql.sock' (2)                       [warning]
Drush was not able to start (bootstrap) the Drupal database.                                                                    [error]
Hint: This error often occurs when Drush is trying to bootstrap a site that has not been installed or does not have a
configured database.

Drush was attempting to connect to : 
  Drupal Root       : /home/username/domains/mywebsite.com/public_html
  Drupal version    : 6.9
  Site Path         : sites/default
  Site URI          : http://public_html
  Database Driver   : mysql
  Database Hostname : localhost

I thought that the "Site URI : http://public_html" might be the problem, but running:
drush --uri=http://mywebsite.com updatecode, produced:

SQLSTATE[HY000] [2002] Can't connect to local MySQL server through socket '/var/lib/mysql/mysql.sock' (2)                       [warning]
Drush was not able to start (bootstrap) the Drupal database.                                                                    [error]
Hint: This error often occurs when Drush is trying to bootstrap a site that has not been installed or does not have a
configured database.

Drush was attempting to connect to : 
  Drupal Root       : /home/username/domains/mywebsite.com/public_html
  Drupal version    : 6.9
  Site Path         : sites/default
  Site URI          : http://mywebsite.com
  Database Driver   : mysql
  Database Hostname : localhost

Any idea of what's causing this? Thanks.