Is there a difference in Google's site indexing, or better question, what is the difference?

Example,

I do a search for a new site I'm trying to get indexed. I use the phrase

site:www.website I'm trying to get indexed.com

And the web site doesn't show as being indexed. I use the phrase

site:website I'm trying to get indexed.com

Without the www. and it shows all of the pages of my new web site as being indexed.

These are non blog sites.

What's the difference?

Thank you