The /search path and the /search/advanced path return only questions, not answers, and by design. It says so right in the doc pages:
Searches a site for any questions which fit the given criteria.
and
This method returns a list of questions.
Your example Stack Overflow search returned answers as well.
The correct equivalent search is:
-- which returns 6 results, the same as the API.
The good news is that, as of version 2.2, the API provides a new route, /search/excerpts, that does return answers also.
If you try it with your raml rest query, you'll see that it gives 18 results -- same as the Stack Overflow search.