What is the difference between limit(1) and range(0, 1)?
Base difference is that range is a method of SelectQuery class, and limit isn't.

Some APIs can extend SelectQuery and add limit. For example  $query-&gt;extendQuery('PagerDefault') will return object of PagerDefault class that has limit method defined.

It may result in a syntax looking like limit() is invoked on SelectQuery, when in fact it isn't:

$query = db_select('node', 'n')
      -&gt;fields('n')
      -&gt;condition('type','problem','=')
      -&gt;extend('PagerDefault')
      -&gt;limit(20);