I didn't understand what you meant by saying can add 'www ahead site:' if you use the site:www.yourdomain.com in Google, you just asked Google what pages did Google indexed in that website.
oh...man, i have type a wrong letter, am means, if we use WWW site:www.yourdomain.com serach in GG, usually we search Google indexed use site:www.yourdomain.com in google, but if we type WWW ahead site:, this result it is right?
Okay, somehow I think I got what you're asking. Just correct me if I'm wrong. When you use "www.yourdomainname.com" in Google, it will display all pages with "www.yourdomain.name" on it. It can be third party websites that talk about your domain name in different ways like in directories if you submitted the same words (i.e. www.yourdomainname.com or even just yourdomainname.com). While using "site:yourdomainname.com", Google will display all pages under your domain name that have been indexed by Google.
u can use your site http and www but u need to edit your ht access file then u can use it otherwise google consider couple site its a disadvantage for your site indexing in google