Replace Docker Hub with Docker where scope is broader than registry

OIDC connections scope access to Docker Hub and Docker Build Cloud,
not just Docker Hub. Keep Docker Hub only where specifically referring
to registry operations.

Author: gmondello

content/actions/how-tos/secure-your-work/security-harden-deployments/oidc-in-docker.md

@@ -1,7 +1,7 @@
 ---
 title: Configuring OpenID Connect in Docker
 shortTitle: OIDC in Docker
-intro: Use OpenID Connect within your workflows to authenticate with Docker Hub without storing long-lived credentials.
+intro: Use OpenID Connect within your workflows to authenticate with Docker without storing long-lived credentials.
 versions:
   fpt: '*'
   ghec: '*'
@@ -12,11 +12,11 @@ category:
 
 ## Overview
 
-OpenID Connect (OIDC) allows your {% data variables.product.prodname_actions %} workflows to authenticate with [Docker Hub](https://hub.docker.com/) to push and pull container images without storing Docker passwords, {% data variables.product.pat_generic_plural %}, or organization access tokens (OATs) in {% data variables.product.company_short %}.
+OpenID Connect (OIDC) allows your {% data variables.product.prodname_actions %} workflows to authenticate with [Docker](https://www.docker.com/) to access Docker Hub and Docker Build Cloud without storing Docker passwords, {% data variables.product.pat_generic_plural %}, or organization access tokens (OATs) in {% data variables.product.company_short %}.
 
 Instead of managing long-lived credentials, you configure a trust relationship between your {% data variables.product.prodname_dotcom %} organization and your Docker organization. When a workflow runs, {% data variables.product.prodname_dotcom %} issues a short-lived OIDC token that Docker validates against your configured rulesets, then issues a scoped access token for the workflow.
 
-This guide gives an overview of how to configure Docker Hub to trust {% data variables.product.prodname_dotcom %}'s OIDC as a federated identity, and demonstrates how to use this configuration in a {% data variables.product.prodname_actions %} workflow.
+This guide gives an overview of how to configure Docker to trust {% data variables.product.prodname_dotcom %}'s OIDC as a federated identity, and demonstrates how to use this configuration in a {% data variables.product.prodname_actions %} workflow.
 
 For more information, see [OIDC connections](https://docs.docker.com/enterprise/security/oidc-connections/) in the Docker documentation.
 
@@ -30,11 +30,11 @@ For more information, see [OIDC connections](https://docs.docker.com/enterprise/
 
 * You must have a Docker Business or Docker Team subscription.
 * You must be an organization owner or editor in your Docker organization.
-* You should plan which repositories, branches, and workflows need access to Docker Hub, and configure rulesets accordingly.
+* You should plan which repositories, branches, and workflows need access to Docker, and configure rulesets accordingly.
 
-## Adding the identity provider to Docker Hub
+## Adding the identity provider to Docker
 
-To use OIDC with Docker, establish a trust relationship between {% data variables.product.prodname_actions %} and Docker Hub by creating an OIDC connection. For more information about this process, see [Create and manage OIDC connections](https://docs.docker.com/enterprise/security/oidc-connections/create-manage/) in the Docker documentation.
+To use OIDC with Docker, establish a trust relationship between {% data variables.product.prodname_actions %} and Docker by creating an OIDC connection. For more information about this process, see [Create and manage OIDC connections](https://docs.docker.com/enterprise/security/oidc-connections/create-manage/) in the Docker documentation.
 
 1. Sign in to [Docker Home](https://app.docker.com/) and navigate to your organization.
 1. Go to **Identity & auth** > **OIDC connections**.
@@ -47,9 +47,9 @@ To use OIDC with Docker, establish a trust relationship between {% data variable
 
 ## Updating your {% data variables.product.prodname_actions %} workflow
 
-Once you have created an OIDC connection in Docker Hub, update your workflow to authenticate using the [`docker/oidc-action`](https://github.com/docker/oidc-action) and [`docker/login-action`](https://github.com/docker/login-action) actions.
+Once you have created an OIDC connection in Docker, update your workflow to authenticate using the [`docker/oidc-action`](https://github.com/docker/oidc-action) and [`docker/login-action`](https://github.com/docker/login-action) actions.
 
-The following example uses the placeholder `YOUR_CONNECTION_ID` for the connection ID you copied from Docker Hub, and `YOUR_DOCKER_ORG` for your Docker organization name.
+The following example uses the placeholder `YOUR_CONNECTION_ID` for the connection ID you copied from Docker, and `YOUR_DOCKER_ORG` for your Docker organization name.
 
 ```yaml
 {% data reusables.actions.actions-not-certified-by-github-comment %}