What resources does a Console control?

In short, very little. In truth, the Console is a "window" into the data kept on the Master-Agent machine, which may or may not be the same machine as the Console.

Console commands are really requests to the Master-Agent, which acts as a messenger to Leaf Agents, and to several child processes on the Master-Agent machine itself that perform specific tasks such as patch downloads, file transfers to targets, updating the remediation database, accessing the database, event logging, reporting etc. For more detail, see "What resources does a Master-Agent control?"

You can find out about remote-access, shared-management, connecting to other Master-Agents, and other details of Console usage.