The first four options represent the very basic behavior of how the keywords should be handled:
Max. results (default: 10) - the number of maximum results in the search box
Show exact matches only (default: Off) - if enabled, the search will return only exactly matching phrases. This feature is not available if the index table engine.
Keyword logic (default: OR) - defines the logical operator used between multiple search phrases. More info in the keyword logic section of this documentation.
Category/Term logic (default: AND) - defines the logical operator between available terms per taxonomy of a post.
AND - displays the result only if each of the terms (for example categories) match.
If any of the categories matching the post is excluded or unchecked on the front-end, the result is not displayed.
OR - displays the result if at least one of the terms (for example categories) match. If at least one category is not excluded where the post belongs, it will be displayed.