Update docs about `script` parameter (#27010)

Added a description of short script form. Also removed references to the obsolete `script.default_lang`.

docs/reference/docs/update-by-query.asciidoc

@@ -98,8 +98,8 @@ parameter in the same way as the search api.
 So far we've only been updating documents without changing their source. That
 is genuinely useful for things like
 <<picking-up-a-new-property,picking up new properties>> but it's only half the
-fun. `_update_by_query` supports a `script` object to update the document. This
-will increment the `likes` field on all of kimchy's tweets:
+fun. `_update_by_query` <<modules-scripting-using,supports scripts>> to update
+the document. This will increment the `likes` field on all of kimchy's tweets:
 
 [source,js]
 --------------------------------------------------

docs/reference/modules/scripting/using.asciidoc

@@ -49,10 +49,7 @@ GET my_index/_search
 
 `lang`::
 
-    Specifies the language the script is written in.  Defaults to `painless` but
-    may be set to any of languages listed in <<modules-scripting>>. The
-    default language may be changed in the `elasticsearch.yml` config file by
-    setting `script.default_lang` to the appropriate language.
+    Specifies the language the script is written in.  Defaults to `painless`.
 
 
 `source`, `id`::
@@ -108,6 +105,30 @@ minute will be compiled. You can change this setting dynamically by setting
 
 ========================================
 
+[float]
+[[modules-scripting-short-script-form]]
+=== Short Script Form
+A short script form can be used for brevity. In the short form, `script` is represented
+by a string instead of an object. This string contains the source of the script.
+
+Short form:
+
+[source,js]
+----------------------
+  "script": "ctx._source.likes++"
+----------------------
+// NOTCONSOLE
+
+The same script in the normal form:
+
+[source,js]
+----------------------
+  "script": {
+    "source": "ctx._source.likes++"
+  }
+----------------------
+// NOTCONSOLE
+
 [float]
 [[modules-scripting-stored-scripts]]
 === Stored Scripts