[DOCS] Reformat rank feature query. Add relevance score section. (#44975)

Author: jrodewig

docs/reference/query-dsl/query_filter_context.asciidoc

@@ -1,27 +1,38 @@
 [[query-filter-context]]
 == Query and filter context
 
-The behaviour of a query clause depends on whether it is used in _query context_ or
-in _filter context_:
+[float]
+[[relevance-scores]]
+=== Relevance scores
 
-Query context::
-+
---
-A query clause used in query context answers the question ``__How well does this
+By default, Elasticsearch sorts matching search results by **relevance
+score**, which measures how well each document matches a query.
+
+The relevance score is a positive floating point number, returned in the
+`_score` meta-field of the <<search-request-body,search>> API. The higher the
+`_score`, the more relevant the document. While each query type can calculate
+relevance scores differently, score calculation also depends on whether the
+query clause is run in a **query** or **filter** context.
+
+[float]
+[[query-context]]
+=== Query context
+In the query context, a query clause answers the question ``__How well does this
 document match this query clause?__'' Besides deciding whether or not the
-document matches, the query clause also calculates a `_score` representing how
-well the document matches, relative to other documents.
+document matches, the query clause also calculates a relevance score in the
+`_score` meta-field.
 
-Query context is in effect whenever a query clause is passed to a `query` parameter,
-such as the `query` parameter in the <<search-request-query,`search`>> API.
---
+Query context is in effect whenever a query clause is passed to a `query`
+parameter, such as the `query` parameter in the
+<<search-request-body,search>> API.
 
-Filter context::
-+
---
-In _filter_ context, a query clause answers the question ``__Does this document
-match this query clause?__''  The answer is a simple Yes or No -- no scores are
-calculated.  Filter context is mostly used for filtering structured data, e.g.
+[float]
+[[filter-context]]
+=== Filter context
+In a filter context, a query clause answers the question ``__Does this
+document match this query clause?__''  The answer is a simple Yes or No -- no
+scores are calculated.  Filter context is mostly used for filtering structured
+data, e.g.
 
 *  __Does this +timestamp+ fall into the range 2015 to 2016?__
 *  __Is the +status+  field set to ++"published"++__?
@@ -34,8 +45,10 @@ parameter, such as the `filter` or `must_not` parameters in the
 <<query-dsl-bool-query,`bool`>> query, the `filter` parameter in the
 <<query-dsl-constant-score-query,`constant_score`>> query, or the
 <<search-aggregations-bucket-filter-aggregation,`filter`>> aggregation.
---
 
+[float]
+[[query-filter-context-ex]]
+=== Example of query and filter contexts
 Below is an example of query clauses being used in query and filter context
 in the `search` API.  This query will match documents where all of the following
 conditions are met:
@@ -75,4 +88,4 @@ GET /_search
 
 TIP: Use query clauses in query context for conditions which should affect the
 score of matching documents (i.e. how well does the document match), and use
-all other query clauses in filter context.
+all other query clauses in filter context.