diff --git a/CHANGELOG.rst b/CHANGELOG.rst
index 1e08562b..78330d29 100644
--- a/CHANGELOG.rst
+++ b/CHANGELOG.rst
@@ -19,6 +19,7 @@ Behavior adaptations:
 * Adjust arbitrary equality intersection preservation in ``SpecifierSet`` (:pull:`951`)
 * Return ``False`` instead of raising for ``.contains`` with invalid version (:pull:`932`)
 * Support arbitrary equality on arbitrary strings for ``Specifier`` and ``SpecifierSet``'s ``filter`` and ``contains`` method. (:pull:`954`)
+* Only try to parse as ``Version`` on certain marker keys, return ``False`` on unequal ordered comparisons (:pull:`939`)
 
 Fixes:
 
diff --git a/src/packaging/markers.py b/src/packaging/markers.py
index 2ae53358..ca3706fe 100644
--- a/src/packaging/markers.py
+++ b/src/packaging/markers.py
@@ -29,6 +29,12 @@
 Operator = Callable[[str, Union[str, AbstractSet[str]]], bool]
 EvaluateContext = Literal["metadata", "lock_file", "requirement"]
 MARKERS_ALLOWING_SET = {"extras", "dependency_groups"}
+MARKERS_REQUIRING_VERSION = {
+    "implementation_version",
+    "platform_release",
+    "python_full_version",
+    "python_version",
+}
 
 
 class InvalidMarker(ValueError):
@@ -177,25 +183,26 @@ def _format_marker(
 _operators: dict[str, Operator] = {
     "in": lambda lhs, rhs: lhs in rhs,
     "not in": lambda lhs, rhs: lhs not in rhs,
-    "<": operator.lt,
-    "<=": operator.le,
+    "<": lambda _lhs, _rhs: False,
+    "<=": operator.eq,
     "==": operator.eq,
     "!=": operator.ne,
-    ">=": operator.ge,
-    ">": operator.gt,
+    ">=": operator.eq,
+    ">": lambda _lhs, _rhs: False,
 }
 
 
-def _eval_op(lhs: str, op: Op, rhs: str | AbstractSet[str]) -> bool:
-    if isinstance(rhs, str):
+def _eval_op(lhs: str, op: Op, rhs: str | AbstractSet[str], *, key: str) -> bool:
+    op_str = op.serialize()
+    if key in MARKERS_REQUIRING_VERSION:
         try:
-            spec = Specifier(f"{op.serialize()}{rhs}")
+            spec = Specifier(f"{op_str}{rhs}")
         except InvalidSpecifier:
             pass
         else:
             return spec.contains(lhs, prereleases=True)
 
-    oper: Operator | None = _operators.get(op.serialize())
+    oper: Operator | None = _operators.get(op_str)
     if oper is None:
         raise UndefinedComparison(f"Undefined {op!r} on {lhs!r} and {rhs!r}.")
 
@@ -242,9 +249,10 @@ def _evaluate_markers(
                 lhs_value = lhs.value
                 environment_key = rhs.value
                 rhs_value = environment[environment_key]
+
             assert isinstance(lhs_value, str), "lhs must be a string"
             lhs_value, rhs_value = _normalize(lhs_value, rhs_value, key=environment_key)
-            groups[-1].append(_eval_op(lhs_value, op, rhs_value))
+            groups[-1].append(_eval_op(lhs_value, op, rhs_value, key=environment_key))
         elif marker == "or":
             groups.append([])
         elif marker == "and":
diff --git a/tests/test_markers.py b/tests/test_markers.py
index c7aa068a..5a9ca9e6 100644
--- a/tests/test_markers.py
+++ b/tests/test_markers.py
@@ -80,10 +80,25 @@ def test_base_class(self) -> None:
 
 class TestOperatorEvaluation:
     def test_prefers_pep440(self) -> None:
-        assert Marker('"2.7.9" < "foo"').evaluate(dict(foo="2.7.10"))
+        assert Marker('"2.7.9" < python_full_version').evaluate(
+            dict(python_full_version="2.7.10")
+        )
+        assert not Marker('"2.7.9" < python_full_version').evaluate(
+            dict(python_full_version="2.7.8")
+        )
 
-    def test_falls_back_to_python(self) -> None:
-        assert Marker('"b" > "a"').evaluate(dict(a="a"))
+    def test_new_string_rules(self) -> None:
+        assert not Marker('"b" < python_full_version').evaluate(
+            dict(python_full_version="c")
+        )
+        assert not Marker('"b" < python_full_version').evaluate(
+            dict(python_full_version="a")
+        )
+        assert not Marker('"b" > "a"').evaluate(dict(a="a"))
+        assert not Marker('"b" < "a"').evaluate(dict(a="a"))
+        assert not Marker('"b" >= "a"').evaluate(dict(a="a"))
+        assert not Marker('"b" <= "a"').evaluate(dict(a="a"))
+        assert Marker('"a" <= "a"').evaluate(dict(a="a"))
 
     def test_fails_when_undefined(self) -> None:
         with pytest.raises(UndefinedComparison):
@@ -443,3 +458,24 @@ def test_extras_and_dependency_groups_disallowed(self, variable: str) -> None:
 
         with pytest.raises(KeyError):
             marker.evaluate(context="requirement")
+
+    @pytest.mark.parametrize(
+        ("marker_string", "environment", "expected"),
+        [
+            ('extra == "v2"', None, False),
+            ('extra == "v2"', {"extra": ""}, False),
+            ('extra == "v2"', {"extra": "v2"}, True),
+            ('extra == "v2"', {"extra": "v2a3"}, False),
+            ('extra == "v2a3"', {"extra": "v2"}, False),
+            ('extra == "v2a3"', {"extra": "v2a3"}, True),
+        ],
+    )
+    def test_version_like_equality(
+        self, marker_string: str, environment: dict[str, str] | None, expected: bool
+    ) -> None:
+        """
+        Test for issue #938: Extras are meant to be literal strings, even if
+        they look like versions, and therefore should not be parsed as version.
+        """
+        marker = Marker(marker_string)
+        assert marker.evaluate(environment) is expected