Address review: fix/add links, document single-phase lookup key

Author: itamaro

Doc/c-api/extension-modules.rst

@@ -323,6 +323,11 @@ in the following ways:
   again.
   Instead, it creates a new module object with a new ``__dict__``, and copies
   the saved contents to it.
+  Modules are matched to the saved contents by the module's full dotted
+  name; the initialization function used is not taken into account.
+
+  As part of the first initialization, Python also adds the module to
+  :data:`sys.modules` under its name.
   For example, given a single-phase module ``_testsinglephase``
   [#testsinglephase]_ that defines a function ``sum`` and an exception class
   ``error``:

Doc/c-api/import.rst

@@ -408,7 +408,7 @@ Importing Modules
 
    *spec* must be a :class:`~importlib.machinery.ModuleSpec` object.
 
-   *initfunc* must be an :ref:`initialization function <extension-export-hook>`,
+   *initfunc* must be an :ref:`initialization function <extension-pyinit>`,
    the same as for :c:func:`PyImport_AppendInittab`.
 
    On success, create and return a module object.
@@ -417,19 +417,16 @@ Importing Modules
    (Custom importers should do this in their
    :py:meth:`~importlib.abc.Loader.exec_module` method.)
 
-   If *initfunc* uses legacy single-phase initialization (that is, it
-   creates the module with :c:func:`PyModule_Create`), the module is fully
-   initialized by *initfunc* itself, and it is also added to
-   :data:`sys.modules` under the spec's name, as is done for modules
-   registered with :c:func:`PyImport_AppendInittab`.
+   If *initfunc* uses
+   :ref:`legacy single-phase initialization <single-phase-initialization>`,
+   the module is fully initialized by *initfunc* itself, and it is also
+   added to :data:`sys.modules` under the spec's name.
    Calling :c:func:`PyModule_Exec` on such a module is still safe.
-
-   The spec's name identifies the module for the purposes of the import
-   system, in the same way as for built-in modules.
-   If a single-phase init module was previously created under the same name
-   (by this function, or in another interpreter), the existing module
-   definition is reused and *initfunc* is not called, so a later call with
-   the same name but a different *initfunc* has no effect.
+   As with any single-phase module, the spec's name identifies the module:
+   if a single-phase module was previously created under the same name
+   (by this function, or in another interpreter), Python does not call
+   *initfunc* again but reuses the saved module contents, so a later call
+   with the same name but a different *initfunc* has no effect.
 
    On error, return NULL with an exception set.