Rules governing views-based free text search
The rules controlling exposed text field filters are various SQL operators. To give you a good indication of what's happening, navigate to admin/structure/views/settings and enable Show the SQL query option for the Views UI then preview various views with different operators. As you enter different text, you can see the SQL keywords used to filter the view.

For Search: Search terms filter its based off the core Search index. The search module crawls node content, breaks it into text tokens, weights the score according to your settings (see admin/config/search/settings), and builds an index for terms to content. 

In terms of fuzzy search technology Drupal's is pretty basic, but it works most of the time. If you're looking for more robust search options there are more advanced solutions out there (Google CSE, Apache Solr, etc.).