diff --git a/README.md b/README.md
index bd6f5a4..5ee06cb 100644
--- a/README.md
+++ b/README.md
@@ -62,20 +62,25 @@ The secret used in `${{ secrets.PYPI_API_TOKEN }}` needs to be created on the
 settings page of your project on GitHub. See [Creating & using secrets].
 
 
-### Publishing with OpenID Connect
+### Trusted publishing
 
 > **IMPORTANT**: This functionality is in beta, and will not work for you
-> unless you're a member of the PyPI OIDC beta testers' group. For more
-> information, see [warehouse#12965].
+> unless you're a member of the PyPI trusted publishing beta testers' group.
+> For more information, see [warehouse#12965].
 
-This action supports PyPI's [OpenID Connect publishing]
+> **NOTE**: Trusted publishing is sometimes referred to by its
+> underlying technology -- OpenID Connect, or OIDC for short.
+> If you see references to "OIDC publishing" in the context of PyPI,
+> this is what they're referring to.
+
+This action supports PyPI's [trusted publishing]
 implementation, which allows authentication to PyPI without a manually
 configured API token or username/password combination. To perform
-[OIDC publishing][OpenID Connect Publishing] with this action, your project's
-OIDC publisher must already be configured on PyPI.
+[trusted publishing] with this action, your project's
+publisher must already be configured on PyPI.
 
-To enter the OIDC flow, configure this action's job with the `id-token: write`
-permission and **without** an explicit username or password:
+To enter the trusted publishing flow, configure this action's job with the
+`id-token: write` permission and **without** an explicit username or password:
 
 ```yaml
 jobs:
@@ -83,7 +88,7 @@ jobs:
     name: Upload release to PyPI
     runs-on: ubuntu-latest
     permissions:
-      id-token: write  # IMPORTANT: this permission is mandatory for OIDC publishing
+      id-token: write  # IMPORTANT: this permission is mandatory for trusted publishing
     steps:
     # retrieve your distributions here
 
@@ -91,7 +96,7 @@ jobs:
       uses: pypa/gh-action-pypi-publish@release/v1
 ```
 
-Other indices that support OIDC publishing can also be used, like TestPyPI:
+Other indices that support trusted publishing can also be used, like TestPyPI:
 
 ```yaml
 - name: Publish package distributions to TestPyPI
@@ -268,4 +273,4 @@ https://raw.githubusercontent.com/vshymanskyy/StandWithUkraine/main/banner-direc
 https://github.com/vshymanskyy/StandWithUkraine/blob/main/docs/README.md
 
 [warehouse#12965]: https://github.com/pypi/warehouse/issues/12965
-[OpenID Connect Publishing]: https://pypi.org/help/#openid-connect
+[trusted publishing]: https://docs.pypi.org/trusted-publishers/
diff --git a/oidc-exchange.py b/oidc-exchange.py
index 52bee14..07579d0 100644
--- a/oidc-exchange.py
+++ b/oidc-exchange.py
@@ -13,7 +13,7 @@ _GITHUB_STEP_SUMMARY = Path(os.getenv("GITHUB_STEP_SUMMARY"))
 # The top-level error message that gets rendered.
 # This message wraps one of the other templates/messages defined below.
 _ERROR_SUMMARY_MESSAGE = """
-Trusted publisher (OIDC) exchange failure:
+Trusted publishing exchange failure:
 
 {message}
 
@@ -24,11 +24,14 @@ publishing, then you should double-check your secret configuration and variable
 names.
 
 Read more about trusted publishers at https://docs.pypi.org/trusted-publishers/
+
+Read more about how this action uses trusted publishers at
+https://github.com/marketplace/actions/pypi-publish#trusted-publishing
 """
 
 # Rendered if OIDC identity token retrieval fails for any reason.
 _TOKEN_RETRIEVAL_FAILED_MESSAGE = """
-OIDC token retrieval failed: {identity_error}
+OpenID Connect token retrieval failed: {identity_error}
 
 This generally indicates a workflow configuration error, such as insufficient
 permissions. Make sure that your workflow has `id-token: write` configured
@@ -71,7 +74,7 @@ def die(msg: str) -> NoReturn:
     with _GITHUB_STEP_SUMMARY.open("a", encoding="utf-8") as io:
         print(_ERROR_SUMMARY_MESSAGE.format(message=msg), file=io)
 
-    print(f"::error::OIDC exchange failure: {msg}", file=sys.stderr)
+    print(f"::error::Trusted publishing exchange failure: {msg}", file=sys.stderr)
     sys.exit(1)
 
 
@@ -94,12 +97,14 @@ def assert_successful_audience_call(resp: requests.Response, domain: str):
         case HTTPStatus.FORBIDDEN:
             # This index supports OIDC, but forbids the client from using
             # it (either because it's disabled, limited to a beta group, etc.)
-            die(f"audience retrieval failed: repository at {domain} has OIDC disabled")
+            die(
+                f"audience retrieval failed: repository at {domain} has trusted publishing disabled",
+            )
         case HTTPStatus.NOT_FOUND:
             # This index does not support OIDC.
             die(
                 "audience retrieval failed: repository at "
-                f"{domain} does not indicate OIDC support",
+                f"{domain} does not indicate trusted publishing support",
             )
         case other:
             status = HTTPStatus(other)
@@ -124,7 +129,7 @@ assert_successful_audience_call(audience_resp, repository_domain)
 
 oidc_audience = audience_resp.json()["audience"]
 
-debug(f"selected OIDC token exchange endpoint: {token_exchange_url}")
+debug(f"selected trusted publishing exchange endpoint: {token_exchange_url}")
 
 try:
     oidc_token = id.detect_credential(audience=oidc_audience)
diff --git a/twine-upload.sh b/twine-upload.sh
index f38d429..bf48246 100755
--- a/twine-upload.sh
+++ b/twine-upload.sh
@@ -44,7 +44,7 @@ if [[ "${INPUT_USER}" == "__token__" && -z "${INPUT_PASSWORD}" ]] ; then
     # No password supplied by the user implies that we're in the OIDC flow;
     # retrieve the OIDC credential and exchange it for a PyPI API token.
     echo \
-        '::notice::Attempting to perform OIDC credential exchange' \
+        '::notice::Attempting to perform trusted publishing exchange' \
         'to retrieve a temporary short-lived API token for authentication' \
         "against ${INPUT_REPOSITORY_URL} due to __token__ username with no" \
         'supplied password field'