REGR: fix op(frame, frame2) with reindex

pandas/core/ops/__init__.py

@@ -722,13 +722,28 @@ def _arith_method_FRAME(cls, op, special):
     @Appender(doc)
     def f(self, other, axis=default_axis, level=None, fill_value=None):
 
+        orig_self, orig_other = self, other
         self, other = _align_method_FRAME(self, other, axis, flex=True, level=level)
 
         if isinstance(other, ABCDataFrame):
             # Another DataFrame
             pass_op = op if should_series_dispatch(self, other, op) else na_op
             pass_op = pass_op if not is_logical else op
 
+            if isinstance(orig_other, ABCDataFrame):
+                if fill_value is None and level is None and axis is default_axis:
+                    # TODO: any other cases we should handle here?
+                    cols = orig_self.columns.intersection(orig_other.columns)
+                    if not (
+                        cols.equals(orig_self.columns)
+                        and cols.equals(orig_other.columns)
+                    ):
+                        # GH#31623, only operate on shared columns
+                        new_left = orig_self[cols]
+                        new_right = orig_other[cols]
+                        result = op(new_left, new_right)
+                        return result.reindex(self.columns, axis=1)
+
             new_data = self._combine_frame(other, pass_op, fill_value)
             return self._construct_result(new_data)
 

pandas/tests/frame/test_arithmetic.py

@@ -711,6 +711,25 @@ def test_operations_with_interval_categories_index(self, all_arithmetic_operator
         expected = pd.DataFrame([[getattr(n, op)(num) for n in data]], columns=ind)
         tm.assert_frame_equal(result, expected)
 
+    def test_frame_with_frame_reindex(self):
+        # GH#31623
+        df = pd.DataFrame(
+            {
+                "foo": [pd.Timestamp("2019"), pd.Timestamp("2020")],
+                "bar": [pd.Timestamp("2018"), pd.Timestamp("2021")],
+            },
+            columns=["foo", "bar"],
+        )
+        df2 = df[["foo"]]
+
+        result = df - df2
+
+        expected = pd.DataFrame(
+            {"foo": [pd.Timedelta(0), pd.Timedelta(0)], "bar": [np.nan, np.nan]},
+            columns=["bar", "foo"],
+        )
+        tm.assert_frame_equal(result, expected)
+
 
 def test_frame_with_zero_len_series_corner_cases():
     # GH#28600