Converted Clicks means that Google will only register one conversion per click on an Ad despite which conversion code the click converts with.  This works great when there is only value in having one unique conversion per customer (i.e. a lead for a software client only has value the first time the form is filled out).

Unlike Converted Clicks, Conversions are recorded multiple times from the same customer after the first click.  This is always the way to record conversions for an eCommerce client, because the only way to trigger the conversion tracking script is by completing the shopping cart (meaning the client is making money for every conversion, and it should be tied to the initial ad spend).