Fixed #22217 - ManyToManyField.through_fields fixes.

- Docs description of arguments mix up.
- Keep it from erroneously masking E332 check.
- Add checks E338 and E339, tweak message of E337.

docs/ref/checks.txt

@@ -94,7 +94,9 @@ Related Fields
 * **fields.E334**: The model is used as an intermediate model by ``<model>``, but it has more than one foreign key from ``<model>``, which is ambiguous. You must specify which foreign key Django should use via the through_fields keyword argument.
 * **fields.E335**: The model is used as an intermediate model by ``<model>``, but it has more than one foreign key to ``<model>``, which is ambiguous. You must specify which foreign key Django should use via the through_fields keyword argument.
 * **fields.E336**: The model is used as an intermediary model by ``<model>``, but it does not have foreign key to ``<model>`` or ``<model>``.
-* **fields.E337**: The field is given an iterable for through_fields, which does not provide the names for both link fields that Django should use for the relation through <model>.
+* **fields.E337**: Field specifies ``through_fields`` but does not provide the names of the two link fields that should be used for the relation through ``<model>``.
+* **fields.E338**: The intermediary model ``<through model>`` has no field ``<field name>``.
+* **fields.E339**: ``<model>.<field name>`` is not a foreign key to ``<model>``.
 
 Signals
 ~~~~~~~

docs/ref/models/fields.txt

@@ -1353,11 +1353,11 @@ that control how the relationship functions.
 
         class Group(models.Model):
             name = models.CharField(max_length=128)
-            members = models.ManyToManyField(Person, through='Membership', through_fields=('person', 'group'))
+            members = models.ManyToManyField(Person, through='Membership', through_fields=('group', 'person'))
 
         class Membership(models.Model):
-            person = models.ForeignKey(Person)
             group = models.ForeignKey(Group)
+            person = models.ForeignKey(Person)
             inviter = models.ForeignKey(Person, related_name="membership_invites")
             invite_reason = models.CharField(max_length=64)
 
@@ -1368,9 +1368,10 @@ that control how the relationship functions.
     above.
 
     ``through_fields`` accepts a 2-tuple ``('field1', 'field2')``, where
-    ``field1`` is the name of the foreign key to the target model (``person``
-    in this case), and ``field2`` the name of the foreign key to the model the
-    :class:`ManyToManyField` is defined on (``group`` in this case).
+    ``field1`` is the name of the foreign key to the model the
+    :class:`ManyToManyField` is defined on (``group`` in this case), and
+    ``field2`` the name of the foreign key to the target model (``person``
+    in this case).
 
     When you have more than one foreign key on an intermediary model to any
     (or even both) of the models participating in a many-to-many relationship,