Google search results via their API vary greatly versus the results from the web interface (as an anonymous, not-logged-in user). This has been reported by others, but here is a direct test performed by me. We are fortunate in this example that the first two results are the same (albeit in reverse order). However the next results bear no resemblance to each other whatsoever.
The default Web UI returns 10 results at a time (on a page).
The default AJAX API returns 4 results at a time, and so was repeated twice advancing by four for the second result set.