simplify the fix, add issue reference number to corresponding test and tighten the wording in doc whatsnew

Author: funnycrab

doc/source/whatsnew/v0.21.0.txt

@@ -130,7 +130,7 @@ Numeric
 Categorical
 ^^^^^^^^^^^
 
-- Bug in ``Categorical.is_dtype_equal()`` where comparison with Series whose dtype is 'category' is not handled correctly (:issue:`16659`)
+- Bug in ``Categorical.is_dtype_equal()`` where comparison with a Series with dtype='category' (:issue:`16659`)
 
 
 Other

pandas/core/categorical.py

@@ -2005,12 +2005,10 @@ def is_dtype_equal(self, other):
             from pandas.core.series import Series
 
             if isinstance(other, Series):
-                other_categorical = other.values
-            else:
-                other_categorical = other
+                other = Categorical(other)
 
-            return (self.categories.equals(other_categorical.categories) and
-                    self.ordered == other_categorical.ordered)
+            return (self.categories.equals(other.categories) and
+                    self.ordered == other.ordered)
         except (AttributeError, TypeError):
             return False
 

pandas/tests/test_categorical.py

@@ -152,6 +152,7 @@ def test_is_equal_dtype(self):
             CategoricalIndex(c1, categories=list('cab'))))
         assert not c1.is_dtype_equal(CategoricalIndex(c1, ordered=True))
 
+        # GH 16659
         s1 = pd.Series(c1)
         assert c1.is_dtype_equal(s1)
         assert not c2.is_dtype_equal(s1)