diff --git a/doc/source/whatsnew/v1.3.0.rst b/doc/source/whatsnew/v1.3.0.rst
index ce64940d964ca..fbd2c2b5345fc 100644
--- a/doc/source/whatsnew/v1.3.0.rst
+++ b/doc/source/whatsnew/v1.3.0.rst
@@ -133,7 +133,7 @@ See :ref:`install.dependencies` and :ref:`install.optional_dependencies` for mor
 
 Other API changes
 ^^^^^^^^^^^^^^^^^
-
+- Partially initialized :class:`CategoricalDtype` (i.e. those with ``categories=None`` objects will no longer compare as equal to fully initialized dtype objects.
 -
 -
 
diff --git a/pandas/core/arrays/categorical.py b/pandas/core/arrays/categorical.py
index 413309b3d01ad..24cbbd9ec6ac9 100644
--- a/pandas/core/arrays/categorical.py
+++ b/pandas/core/arrays/categorical.py
@@ -36,6 +36,7 @@
     is_scalar,
     is_timedelta64_dtype,
     needs_i8_conversion,
+    pandas_dtype,
 )
 from pandas.core.dtypes.dtypes import CategoricalDtype
 from pandas.core.dtypes.generic import ABCIndex, ABCSeries
@@ -409,6 +410,7 @@ def astype(self, dtype: Dtype, copy: bool = True) -> ArrayLike:
             If copy is set to False and dtype is categorical, the original
             object is returned.
         """
+        dtype = pandas_dtype(dtype)
         if self.dtype is dtype:
             result = self.copy() if copy else self
 
diff --git a/pandas/core/dtypes/common.py b/pandas/core/dtypes/common.py
index 081339583e3fd..5869b2cf22516 100644
--- a/pandas/core/dtypes/common.py
+++ b/pandas/core/dtypes/common.py
@@ -639,6 +639,19 @@ def is_dtype_equal(source, target) -> bool:
     >>> is_dtype_equal(DatetimeTZDtype(tz="UTC"), "datetime64")
     False
     """
+    if isinstance(target, str):
+        if not isinstance(source, str):
+            # GH#38516 ensure we get the same behavior from
+            #  is_dtype_equal(CDT, "category") and CDT == "category"
+            try:
+                src = get_dtype(source)
+                if isinstance(src, ExtensionDtype):
+                    return src == target
+            except (TypeError, AttributeError):
+                return False
+    elif isinstance(source, str):
+        return is_dtype_equal(target, source)
+
     try:
         source = get_dtype(source)
         target = get_dtype(target)
diff --git a/pandas/core/dtypes/dtypes.py b/pandas/core/dtypes/dtypes.py
index 0de8a07abbec3..75f3b511bc57d 100644
--- a/pandas/core/dtypes/dtypes.py
+++ b/pandas/core/dtypes/dtypes.py
@@ -354,12 +354,10 @@ def __eq__(self, other: Any) -> bool:
         elif not (hasattr(other, "ordered") and hasattr(other, "categories")):
             return False
         elif self.categories is None or other.categories is None:
-            # We're forced into a suboptimal corner thanks to math and
-            # backwards compatibility. We require that `CDT(...) == 'category'`
-            # for all CDTs **including** `CDT(None, ...)`. Therefore, *all*
-            # CDT(., .) = CDT(None, False) and *all*
-            # CDT(., .) = CDT(None, True).
-            return True
+            # For non-fully-initialized dtypes, these are only equal to
+            #  - the string "category" (handled above)
+            #  - other CategoricalDtype with categories=None
+            return self.categories is other.categories
         elif self.ordered or other.ordered:
             # At least one has ordered=True; equal if both have ordered=True
             # and the same values for categories in the same order.
diff --git a/pandas/tests/arrays/categorical/test_dtypes.py b/pandas/tests/arrays/categorical/test_dtypes.py
index 12654388de904..a2192b2810596 100644
--- a/pandas/tests/arrays/categorical/test_dtypes.py
+++ b/pandas/tests/arrays/categorical/test_dtypes.py
@@ -127,7 +127,7 @@ def test_astype(self, ordered):
         expected = np.array(cat)
         tm.assert_numpy_array_equal(result, expected)
 
-        msg = r"Cannot cast object dtype to <class 'float'>"
+        msg = r"Cannot cast object dtype to float64"
         with pytest.raises(ValueError, match=msg):
             cat.astype(float)
 
diff --git a/pandas/tests/dtypes/test_common.py b/pandas/tests/dtypes/test_common.py
index 0d0601aa542b4..9e75ba0864e76 100644
--- a/pandas/tests/dtypes/test_common.py
+++ b/pandas/tests/dtypes/test_common.py
@@ -641,7 +641,6 @@ def test_is_complex_dtype():
         (pd.CategoricalIndex(["a", "b"]).dtype, CategoricalDtype(["a", "b"])),
         (pd.CategoricalIndex(["a", "b"]), CategoricalDtype(["a", "b"])),
         (CategoricalDtype(), CategoricalDtype()),
-        (CategoricalDtype(["a", "b"]), CategoricalDtype()),
         (pd.DatetimeIndex([1, 2]), np.dtype("=M8[ns]")),
         (pd.DatetimeIndex([1, 2]).dtype, np.dtype("=M8[ns]")),
         ("<M8[ns]", np.dtype("<M8[ns]")),
diff --git a/pandas/tests/dtypes/test_dtypes.py b/pandas/tests/dtypes/test_dtypes.py
index 872dd03768833..8ba8562affb67 100644
--- a/pandas/tests/dtypes/test_dtypes.py
+++ b/pandas/tests/dtypes/test_dtypes.py
@@ -90,9 +90,20 @@ def test_hash_vs_equality(self, dtype):
         assert hash(dtype) == hash(dtype2)
 
     def test_equality(self, dtype):
+        assert dtype == "category"
         assert is_dtype_equal(dtype, "category")
+        assert "category" == dtype
+        assert is_dtype_equal("category", dtype)
+
+        assert dtype == CategoricalDtype()
         assert is_dtype_equal(dtype, CategoricalDtype())
+        assert CategoricalDtype() == dtype
+        assert is_dtype_equal(CategoricalDtype(), dtype)
+
+        assert dtype != "foo"
         assert not is_dtype_equal(dtype, "foo")
+        assert "foo" != dtype
+        assert not is_dtype_equal("foo", dtype)
 
     def test_construction_from_string(self, dtype):
         result = CategoricalDtype.construct_from_string("category")
@@ -834,10 +845,27 @@ def test_categorical_equality(self, ordered1, ordered2):
         c1 = CategoricalDtype(list("abc"), ordered1)
         c2 = CategoricalDtype(None, ordered2)
         c3 = CategoricalDtype(None, ordered1)
-        assert c1 == c2
-        assert c2 == c1
+        assert c1 != c2
+        assert c2 != c1
         assert c2 == c3
 
+    def test_categorical_dtype_equality_requires_categories(self):
+        # CategoricalDtype with categories=None is *not* equal to
+        #  any fully-initialized CategoricalDtype
+        first = CategoricalDtype(["a", "b"])
+        second = CategoricalDtype()
+        third = CategoricalDtype(ordered=True)
+
+        assert second == second
+        assert third == third
+
+        assert first != second
+        assert second != first
+        assert first != third
+        assert third != first
+        assert second == third
+        assert third == second
+
     @pytest.mark.parametrize("categories", [list("abc"), None])
     @pytest.mark.parametrize("other", ["category", "not a category"])
     def test_categorical_equality_strings(self, categories, ordered, other):
diff --git a/pandas/tests/reshape/merge/test_merge.py b/pandas/tests/reshape/merge/test_merge.py
index f43ae58fbcc2f..e11edabb2f468 100644
--- a/pandas/tests/reshape/merge/test_merge.py
+++ b/pandas/tests/reshape/merge/test_merge.py
@@ -1622,7 +1622,7 @@ def test_identical(self, left):
         merged = pd.merge(left, left, on="X")
         result = merged.dtypes.sort_index()
         expected = Series(
-            [CategoricalDtype(), np.dtype("O"), np.dtype("O")],
+            [CategoricalDtype(categories=["foo", "bar"]), np.dtype("O"), np.dtype("O")],
             index=["X", "Y_x", "Y_y"],
         )
         tm.assert_series_equal(result, expected)
@@ -1633,7 +1633,11 @@ def test_basic(self, left, right):
         merged = pd.merge(left, right, on="X")
         result = merged.dtypes.sort_index()
         expected = Series(
-            [CategoricalDtype(), np.dtype("O"), np.dtype("int64")],
+            [
+                CategoricalDtype(categories=["foo", "bar"]),
+                np.dtype("O"),
+                np.dtype("int64"),
+            ],
             index=["X", "Y", "Z"],
         )
         tm.assert_series_equal(result, expected)
@@ -1713,7 +1717,11 @@ def test_other_columns(self, left, right):
         merged = pd.merge(left, right, on="X")
         result = merged.dtypes.sort_index()
         expected = Series(
-            [CategoricalDtype(), np.dtype("O"), CategoricalDtype()],
+            [
+                CategoricalDtype(categories=["foo", "bar"]),
+                np.dtype("O"),
+                CategoricalDtype(categories=[1, 2]),
+            ],
             index=["X", "Y", "Z"],
         )
         tm.assert_series_equal(result, expected)