They both achieve the same results but with different approaches. Though you are misusing the ON clause.
I would suggest something like this:
$query = mysql_query("
SELECT table_one.row
FROM table_one
INNER JOIN table_two
ON table_one.id = table_two.id
WHERE table_two.row = $id");
Quote from mysql site:
The conditional_expr used with ON is any conditional expression of the form that can be used in a WHERE clause. Generally, you should use the ON clause for conditions that specify how to join tables, and the WHERE clause to restrict which rows you want in the result set.