bpo-31567: more decorator markup fixes in docs (GH-3959) (#3966)

diff --git a/Doc/library/functions.rst b/Doc/library/functions.rst
index eed6730..e472257 100644
--- a/Doc/library/functions.rst
+++ b/Doc/library/functions.rst
@@ -1419,12 +1419,21 @@
    :func:`classmethod` for a variant that is useful for creating alternate class
    constructors.
 
+   Like all decorators, it is also possible to call ``staticmethod`` as
+   a regular function and do something with its result.  This is needed
+   in some cases where you need a reference to a function from a class
+   body and you want to avoid the automatic transformation to instance
+   method.  For these cases, use this idiom:
+
+      class C:
+          builtin_open = staticmethod(open)
+
    For more information on static methods, consult the documentation on the
    standard type hierarchy in :ref:`types`.
 
-   .. index::
-      single: string; str() (built-in function)
 
+.. index::
+   single: string; str() (built-in function)
 
 .. _func-str:
 .. class:: str(object='')
diff --git a/Doc/library/typing.rst b/Doc/library/typing.rst
index bd04f73..9883d8b 100644
--- a/Doc/library/typing.rst
+++ b/Doc/library/typing.rst
@@ -897,17 +897,17 @@
 
    See :pep:`484` for details and comparison with other typing semantics.
 
-.. decorator:: no_type_check(arg)
+.. decorator:: no_type_check
 
    Decorator to indicate that annotations are not type hints.
 
-   The argument must be a class or function; if it is a class, it
+   This works as class or function :term:`decorator`.  With a class, it
    applies recursively to all methods defined in that class (but not
    to methods defined in its superclasses or subclasses).
 
    This mutates the function(s) in place.
 
-.. decorator:: no_type_check_decorator(decorator)
+.. decorator:: no_type_check_decorator
 
    Decorator to give another decorator the :func:`no_type_check` effect.
 
diff --git a/Lib/test/test_typing.py b/Lib/test/test_typing.py
index 87d707c..a3b6eb9 100644
--- a/Lib/test/test_typing.py
+++ b/Lib/test/test_typing.py
@@ -1471,8 +1471,8 @@
     def test_meta_no_type_check(self):
 
         @no_type_check_decorator
-        def magic_decorator(deco):
-            return deco
+        def magic_decorator(func):
+            return func
 
         self.assertEqual(magic_decorator.__name__, 'magic_decorator')