Google API returning different results than website

This google page has what you are looking for https://support.google.com/customsearch/answer/70392?hl=en

your results are unlikely to match those returned by Google Web Search, for several reasons:

  1. Even if a custom search engine is configured to search the entire web, it’s designed to emphasize results from your own sites.
  2. Your custom search engine doesn’t include Google Web Search features such as Oneboxes, real-time results, universal search, social feaures, or personalized results.
  3. If your custom search engine includes more than ten sites, the results may be from a subset of our index and may differ from the results of a 'site:' search on Google.com.

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Google Api