diff --git a/Doc/distributing/index.rst b/Doc/distributing/index.rst
index 66ba1e9fb9b..136cf4e77b1 100644
--- a/Doc/distributing/index.rst
+++ b/Doc/distributing/index.rst
@@ -31,7 +31,7 @@ installing other Python projects, refer to the
 Key terms
 =========
 
-* the `Python Packaging Index <https://pypi.org>`__ is a public
+* the `Python Package Index <https://pypi.org>`__ is a public
   repository of open source licensed packages made available for use by
   other Python users
 * the `Python Packaging Authority
@@ -127,14 +127,14 @@ involved in creating and publishing a project:
 
 * `Project structure`_
 * `Building and packaging the project`_
-* `Uploading the project to the Python Packaging Index`_
+* `Uploading the project to the Python Package Index`_
 * `The .pypirc file`_
 
 .. _Project structure: \
     https://packaging.python.org/tutorials/packaging-projects/#packaging-python-projects
 .. _Building and packaging the project: \
    https://packaging.python.org/tutorials/packaging-projects/#creating-the-package-files
-.. _Uploading the project to the Python Packaging Index: \
+.. _Uploading the project to the Python Package Index: \
    https://packaging.python.org/tutorials/packaging-projects/#uploading-the-distribution-archives
 .. _The .pypirc file: \
    https://packaging.python.org/specifications/pypirc/
@@ -150,7 +150,7 @@ These are quick answers or links for some common tasks.
 
 This isn't an easy topic, but here are a few tips:
 
-* check the Python Packaging Index to see if the name is already in use
+* check the Python Package Index to see if the name is already in use
 * check popular hosting sites like GitHub, Bitbucket, etc to see if there
   is already a project with that name
 * check what comes up in a web search for the name you're considering
diff --git a/Doc/installing/index.rst b/Doc/installing/index.rst
index 5e7e03045b2..4bacc7ba0c2 100644
--- a/Doc/installing/index.rst
+++ b/Doc/installing/index.rst
@@ -44,7 +44,7 @@ Key terms
   ``venv``. It allows virtual environments to be used on versions of
   Python prior to 3.4, which either don't provide ``venv`` at all, or
   aren't able to automatically install ``pip`` into created environments.
-* The `Python Packaging Index <https://pypi.org>`__ is a public
+* The `Python Package Index <https://pypi.org>`__ is a public
   repository of open source licensed packages made available for use by
   other Python users.
 * the `Python Packaging Authority
@@ -78,7 +78,7 @@ The standard packaging tools are all designed to be used from the command
 line.
 
 The following command will install the latest version of a module and its
-dependencies from the Python Packaging Index::
+dependencies from the Python Package Index::
 
     python -m pip install SomePackage
 
@@ -226,7 +226,7 @@ the installation process.
 
 With the introduction of support for the binary ``wheel`` format, and the
 ability to publish wheels for at least Windows and macOS through the
-Python Packaging Index, this problem is expected to diminish over time,
+Python Package Index, this problem is expected to diminish over time,
 as users are more regularly able to install pre-built extensions rather
 than needing to build them themselves.