Defining the problem:
  1. It is not obvious to the user that entering multiple words in the Quick Search will not find the issue if each word is in a different standard text field. This is also an issue if one word is in a standard text field and the other is in a custom text field. The only reference to this behavior I saw is the blue information box in the NOT section of this page:
 
https://confluence.atlassian.com/jiracoreserver073/search-syntax-for-text-fields-861257223.html#Searchsyntaxfortextfields-NOT
 
  2. In order to search for multiple words, each of which can appear individually in separate standard (or custom) text fields, users must write JQL. There should be an easier way to tell the system to search for multiple words and include JIRAs where the words appear in separate text fields.
 
Suggested solution:
  If a user enters multiple words in the Quick Search, there should be a popup message (like the Smart Search popup) or an info box stating "Only showing JIRAs for which all words appear in the same text field (all words appear in the Summary, or all words appear in the Comments, etc). To search for JIRAs without this restriction, click here". Clicking the link should change the JQL from:
 
    text ~ "word1 word2 [... wordN]"
    
    To:
    
    text ~ "word1" AND text ~ "word2" ... AND text ~ "wordN"
 
Additionally, there should be more robust options for doing a text search on the JIRA Search page. I would suggest there should be a "Text Search" button next to the Basic/Advanced link. This should show options (maybe right on the page, maybe via a popup, or maybe on a separate page altogether) to allow users to do a text search exactly the way they want, without having to enter it in the quick search and then click the link from the popup/info box I am suggesting. And also without having to type in all the JQL themselves. These options should allow users to enter multiple words and phrases, along with AND and OR options, including an option to turn on and off the "all words and phrases must appear in the same text field" functionality.
 
 I feel that both the proposed popup/info box for the Quick Search, as well as the suggested "Text Search" button should be implemented. The Quick Search popup will inform users of how the Quick Search handles multiple words. And the "Text Search" button will provide a robust way to enter text search criteria so users can go directly there if they know the Quick Search won't do what they need.