Search filter result score
There are a few things affecting the difference in results. I'm sure you noticed the queries differ slightly.


The first and core issue is that the search module's main table is search_index, so each row is built around entries in that table and then joined outward to get more information. Your view is built around the node table and joined the other direction to search index.
The core search uses inner joins to get node data, which will be more limiting in its result sets (see this answer.)
The search_dataset table isn't joined from the Views search (see this answer for an explanation of why.)
Core search multiplies the search scores by relevance, which shouldn't affect their ranking, but looks confusing. See line 496-500 of search.extender.inc.


I know I only answered the first half of your question, but I hope this helps. I'm not sure it's possible to get a View to exactly mirror your search results without considerable customization.