I'm going to go out on a limb here and offer my thoughts, but I might be wrong. I'm honestly the last person who ought to be answering this question, but, no one else is offering an answer, and a questionable one is better than none at all.
The reason you're getting regular Google search results with your Google site bar, is that's what it is. They have a massive database, and a way to query it for web pages with a certain key phrase. When you slap a copy on your site, you're still hitting the same database. If they don't know about a particular page during a regular search, they still won't know about it when someone chooses to search your site only.
I think most eCommerce sites use their own internal or 3rd party search engines to accomplish this. Endecca, FAST, DT-Search, etc.
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