Google advises to use one URL for Mobile and Desktop version

For a mobile version of site , do we use a different URL or do we use the same desktop URL for a Mobile template ?
Well Heres Google Advises -> serve smartphone and desktop users from the same URLs, with Special Stylesheet to optimize the content shown on smartphones.

Well Heres Google Advises -> serve smartphone and desktop users from the same URLs, with Special Stylesheet to optimize the content shown on smartphones.
