diff --git a/doc/source/whatsnew/v2.0.0.rst b/doc/source/whatsnew/v2.0.0.rst
index 75ba169600962..f89bcc2c27ed0 100644
--- a/doc/source/whatsnew/v2.0.0.rst
+++ b/doc/source/whatsnew/v2.0.0.rst
@@ -98,6 +98,7 @@ Other enhancements
 - Added :meth:`Index.infer_objects` analogous to :meth:`Series.infer_objects` (:issue:`50034`)
 - Added ``copy`` parameter to :meth:`Series.infer_objects` and :meth:`DataFrame.infer_objects`, passing ``False`` will avoid making copies for series or columns that are already non-object or where no better dtype can be inferred (:issue:`50096`)
 - :meth:`DataFrame.plot.hist` now recognizes ``xlabel`` and ``ylabel`` arguments (:issue:`49793`)
+- Improved error message when trying to align :class:`DataFrame` objects (for example, in :func:`DataFrame.compare`) to clarify that "identically labelled" refers to both index and columns (:issue:`50083`)
 -
 
 .. ---------------------------------------------------------------------------
diff --git a/pandas/core/ops/__init__.py b/pandas/core/ops/__init__.py
index 0be6a13621ab2..3908422bba523 100644
--- a/pandas/core/ops/__init__.py
+++ b/pandas/core/ops/__init__.py
@@ -313,7 +313,8 @@ def to_series(right):
                 left, right = left.align(right, join="outer", level=level, copy=False)
             else:
                 raise ValueError(
-                    "Can only compare identically-labeled DataFrame objects"
+                    "Can only compare identically-labeled (both index and columns) "
+                    "DataFrame objects"
                 )
     elif isinstance(right, ABCSeries):
         # axis=1 is default for DataFrame-with-Series op
diff --git a/pandas/tests/frame/methods/test_compare.py b/pandas/tests/frame/methods/test_compare.py
index 455acde1af684..fe74ec8077bc9 100644
--- a/pandas/tests/frame/methods/test_compare.py
+++ b/pandas/tests/frame/methods/test_compare.py
@@ -170,14 +170,20 @@ def test_compare_multi_index(align_axis):
 
 def test_compare_unaligned_objects():
     # test DataFrames with different indices
-    msg = "Can only compare identically-labeled DataFrame objects"
+    msg = (
+        r"Can only compare identically-labeled \(both index and columns\) DataFrame "
+        "objects"
+    )
     with pytest.raises(ValueError, match=msg):
         df1 = pd.DataFrame([1, 2, 3], index=["a", "b", "c"])
         df2 = pd.DataFrame([1, 2, 3], index=["a", "b", "d"])
         df1.compare(df2)
 
     # test DataFrames with different shapes
-    msg = "Can only compare identically-labeled DataFrame objects"
+    msg = (
+        r"Can only compare identically-labeled \(both index and columns\) DataFrame "
+        "objects"
+    )
     with pytest.raises(ValueError, match=msg):
         df1 = pd.DataFrame(np.ones((3, 3)))
         df2 = pd.DataFrame(np.zeros((2, 1)))
diff --git a/pandas/tests/frame/test_arithmetic.py b/pandas/tests/frame/test_arithmetic.py
index d55843603fb63..241e2df377af6 100644
--- a/pandas/tests/frame/test_arithmetic.py
+++ b/pandas/tests/frame/test_arithmetic.py
@@ -1536,7 +1536,10 @@ def test_comparisons(self, simple_frame, float_frame, func):
         result3 = func(float_frame, 0)
         tm.assert_numpy_array_equal(result3.values, func(float_frame.values, 0))
 
-        msg = "Can only compare identically-labeled DataFrame"
+        msg = (
+            r"Can only compare identically-labeled \(both index and columns\) "
+            "DataFrame objects"
+        )
         with pytest.raises(ValueError, match=msg):
             func(simple_frame, simple_frame[:2])
 
diff --git a/pandas/tests/frame/test_nonunique_indexes.py b/pandas/tests/frame/test_nonunique_indexes.py
index 4c21446cab375..819a8304769ab 100644
--- a/pandas/tests/frame/test_nonunique_indexes.py
+++ b/pandas/tests/frame/test_nonunique_indexes.py
@@ -201,7 +201,10 @@ def test_dup_columns_comparisons(self):
         df2 = DataFrame([[0, 1], [2, 4], [2, np.nan], [4, 5]], columns=["A", "A"])
 
         # not-comparing like-labelled
-        msg = "Can only compare identically-labeled DataFrame objects"
+        msg = (
+            r"Can only compare identically-labeled \(both index and columns\) "
+            "DataFrame objects"
+        )
         with pytest.raises(ValueError, match=msg):
             df1 == df2
 
diff --git a/pandas/tests/series/test_arithmetic.py b/pandas/tests/series/test_arithmetic.py
index 9d8cf9787ad3f..27410a626811c 100644
--- a/pandas/tests/series/test_arithmetic.py
+++ b/pandas/tests/series/test_arithmetic.py
@@ -643,10 +643,19 @@ def test_ne(self):
     )
     def test_comp_ops_df_compat(self, left, right, frame_or_series):
         # GH 1134
-        msg = f"Can only compare identically-labeled {frame_or_series.__name__} objects"
+        # GH 50083 to clarify that index and columns must be identically labeled
         if frame_or_series is not Series:
+            msg = (
+                rf"Can only compare identically-labeled \(both index and columns\) "
+                f"{frame_or_series.__name__} objects"
+            )
             left = left.to_frame()
             right = right.to_frame()
+        else:
+            msg = (
+                f"Can only compare identically-labeled {frame_or_series.__name__} "
+                f"objects"
+            )
 
         with pytest.raises(ValueError, match=msg):
             left == right