Explanation:
Box 1: Azure Update Manager
For update management, use:
Support matrix for Azure Update Manager
Operating system updates
Update Manager supports operating system updates for both Windows and Linux.
Extended Security Updates (ESU) for Windows Server
Using Azure Update Manager, you can deploy Extended Security Updates for your Azure Arc- enabled Windows Server 2012 / R2 machines.
Box 2: The Azure Connected Machine agent
On the on-premises operating systems, install:
The Update Manager extension is installed and managed by using:
Azure VM Windows agent or the Azure VM Linux agent for Azure VMs.
Azure Arc-enabled servers agent (also known as the Azure Connected Machine agent) for non- Azure Linux and Windows machines or physical servers.
The Azure Connected Machine agent enables you to manage your Windows and Linux machines hosted outside of Azure on your corporate network or other cloud providers.
Reference:
https://learn.microsoft.com/en-us/azure/update-manager/support-matrix
https://learn.microsoft.com/en-us/azure/update-manager/overview
https://learn.microsoft.com/en-us/azure/azure-arc/servers/agent-overview