Azure Equivalent for CodeDeploy
Azure has a robust CI/CD pipeline which is much easier to use than CodeDeploy on AWS. It is called Build/Release pipelines under Azure DevOps. It allows you to configure multiple environments with build and release (deployment) stages for each. It also allows for easy configuration and interoperability with Azure Webapps/VMs and other resources available on Azure. Having recently switched from Azure to AWS, I definitely miss the ease of configuration and the intuitive UI on Azure DevOps.

Azure DevOps integrates a version control repository system, a agile style work items/boards which can also be used to configure your backlogs and iteration items. There is even a dashboard to integrate and monitor your work items and deployments across the team. So it is definitely much bigger than just a devops tool or CodeBuild.