Update fuzzy.md (opensearch-project#7842)

* Update fuzzy.md

Corrected the name of the string metric used by default

Signed-off-by: Tim <[email protected]>
Signed-off-by: svitlo <[email protected]>

* correct the line 17 of fuzzy.md to clarify the distance name and the role of the field 'transpositions'

Signed-off-by: svitlo <[email protected]>

* correct the line 17 to not break the thought regarding the usage of the field 'max_expansions'

Signed-off-by: svitlo <[email protected]>

* Update _query-dsl/term/fuzzy.md

Co-authored-by: kolchfa-aws <[email protected]>
Signed-off-by: Tim <[email protected]>
Signed-off-by: svitlo <[email protected]>

---------

Signed-off-by: Tim <[email protected]>
Signed-off-by: svitlo <[email protected]>
Co-authored-by: svitlo <[email protected]>
Co-authored-by: kolchfa-aws <[email protected]>

_query-dsl/term/fuzzy.md

@@ -7,14 +7,14 @@ nav_order: 20
 
 # Fuzzy query
 
-A fuzzy query searches for documents containing terms that are similar to the search term within the maximum allowed [Levenshtein distance](https://en.wikipedia.org/wiki/Levenshtein_distance). The Levenshtein distance measures the number of one-character changes needed to change one term to another term. These changes include:
+A fuzzy query searches for documents containing terms that are similar to the search term within the maximum allowed [Damerau–Levenshtein distance](https://en.wikipedia.org/wiki/Damerau–Levenshtein_distance). The Damerau–Levenshtein distance measures the number of one-character changes needed to change one term to another term. These changes include:
 
 - Replacements: **c**at to **b**at
 - Insertions: cat to cat**s**
 - Deletions: **c**at to at
 - Transpositions: **ca**t to **ac**t
 
-A fuzzy query creates a list of all possible expansions of the search term that fall within the Levenshtein distance. You can specify the maximum number of such expansions in the `max_expansions` field. Then it searches for documents that match any of the expansions.
+A fuzzy query creates a list of all possible expansions of the search term that fall within the Damerau-Levenshtein distance. You can specify the maximum number of such expansions in the `max_expansions` field. The query then searches for documents that match any of the expansions. If you set the `transpositions` parameter to `false`, then your search will use the classic [Levenshtein distance](https://en.wikipedia.org/wiki/Levenshtein_distance). 
 
 The following example query searches for the speaker `HALET` (misspelled `HAMLET`). The maximum edit distance is not specified, so the default `AUTO` edit distance is used:
 
@@ -90,4 +90,4 @@ Specifying a large value in `max_expansions` can lead to poor performance, espec
 {: .warning}
 
 If [`search.allow_expensive_queries`]({{site.url}}{{site.baseurl}}/query-dsl/index/#expensive-queries) is set to `false`, fuzzy queries are not run.
-{: .important}
+{: .important}