Search results by closest match to query
Lots going on here, but I'll take a stab at it (in the future, it's helpful if you have multiple questions/issues to make separate posts for them).

Your questions of "why isn't this search term matching" probably comes down to the fact that by default, Craft doesn't do fuzzy matching.  You can use wildcards (*) to change that behavior on a per-search basis.  You can see that syntax here along with all of the other search syntax that Craft supports: https://craftcms.com/docs/searching

Also of note from that page is the defaultSearchTerms config setting, where you can change that behavior.


  Then my search component is this:


{% set query = craft.request.getParam('q') %}

{% paginate craft.entries.section('Organizations').search('title:' ~ query).order('score').limit(10) as entries %}
    {% if entries|length &lt; 1 %}
        {% paginate craft.entries.section('Organizations').search('organizationSummary:' ~ query).order('score').limit(10) as entries %}


That's probably not working as expected because not only can you not nest paginate tags, you can technically only have one paginate tag per request.