More edits to the intro text

Related to: https://gitlab.com/gitlab-org/gitlab/-/issues/300312

doc/ci/docker/using_docker_build.md

@@ -7,14 +7,14 @@ type: concepts, howto
 
 # Use Docker to build Docker images
 
-You can use GitLab CI/CD with Docker Engine to build and test Docker-based projects.
+You can use GitLab CI/CD with Docker to build and test Docker images.
 
 For example, you might want to:
 
-1. Create an application image.
-1. Run tests against the created image.
-1. Push image to a remote registry.
-1. Deploy to a server from the pushed image.
+1. Create a Docker image of your application.
+1. Run tests against the image.
+1. Push the image to a remote registry.
+1. Use the image to deploy your application to a server.
 
 Or, if your application already has a `Dockerfile`, you can
 use it to create and test an image:
@@ -27,7 +27,7 @@ docker push my-registry:5000/my-image
 ```
 
 To run Docker commands in your CI/CD jobs, you must configure
-GitLab Runner to enable `docker` support.
+GitLab Runner to support `docker` commands.
 
 ## Enable Docker commands in your CI/CD jobs
 

doc/ci/docker/using_docker_images.md

@@ -7,27 +7,23 @@ type: concepts, howto
 
 # Run your CI/CD jobs in Docker containers
 
-GitLab CI/CD in conjunction with [GitLab Runner](../runners/README.md) can use
-[Docker Engine](https://www.docker.com/) to test and build any application.
+You can run your CI/CD jobs in separate, isolated Docker containers.
 
-Docker is an open-source project that has predefined images you can use to
-run applications in independent "containers." These containers run in a single Linux
-instance. [Docker Hub](https://hub.docker.com/) is a database of pre-built images you can
-use to test and build your applications.
+When you run a Docker container on your local machine, it acts as a reproducible build environment.
+You can run tests in the container, instead of testing on a dedicated CI/CD server.
 
-When you use Docker with GitLab CI/CD, Docker runs each job in a separate and isolated
-container. You specify the container image in the project's
-[`.gitlab-ci.yml`](../yaml/README.md) file.
+To run CI/CD jobs in a Docker container, you need to:
 
-Docker containers provide a reproducible build environment that
-can run on your workstation. When a Docker container is running, you can test
-commands from your shell, rather than having to
-test them on a dedicated CI server.
+- Register a runner that uses the Docker executor. Then all jobs run in a Docker container.
+- Specify an image in your `.gitlab-ci.yml` file. The runner creates a container from this image
+  and runs the jobs in it.
+- Optional. Specify other images in your `.gitlab-ci.yml` file. These containers are known as
+  ["services"](#what-is-a-service) and you can use them to run services like MySQL separately.
 
-## Register Docker Runner
+## Register a runner that uses the Docker executor
 
-To use GitLab Runner with Docker you need to [register a new runner](https://docs.gitlab.com/runner/register/)
-to use the `docker` executor.
+To use GitLab Runner with Docker you need to [register a runner](https://docs.gitlab.com/runner/register/)
+that uses the Docker executor.
 
 In this example, we first set up a temporary template to supply the services: