Problem Definition

The result of full search isn't necessarily a superset of quick search.
Sometimes full search doesn't return items that has been hit as a candidates at the quick search.

For example, here is the step to reproduce. 

1. Create a page with a name "ABCDEF".
2. On the quick search, type "ABC"
   
3. Click "search for 'ABC'" on the dropdown
   

As above, this quick search returns "ABCDEF" while full search doesn't.

Suggested Solution

In the example above, expected behavior should be any of the following.

• Both quick and full search result contains the "ABCDEF".
  or
• Both quick and full search result doesn't contain the "ABCDEF".
  or
• Full search returns the "ABCDEF" while quick search doesn't.

To achieve the requirement above, three possible solutions are suggested.

• Let quick search access to lucene with same condition as full search.
  or
• Tune the full search (lucene) to cover the quick search result.
  or
• Tune the quick search to limit the result not to return the items that shall not be contained in full search.

Why this is important

Because it's not intuitive.
In many cases quick search is used first to enter full search, so it looks like the search result was lost in the full search.

Note

In the example above, appending an asterisk in the query like "ABC*" enables full search to return the "ABCDEF".
(Please note this doesn't cover all search query string.)

This is based on the specification of CQL.
https://developer.atlassian.com/server/confluence/performing-text-searches-using-cql/

Note 2

The definitions of the quick and full search are in https://confluence.atlassian.com/doc/search-139528.html