What is the Difference Between "Running" and "Connected" Server Status with MuleSoft Runtime Manager

For on-prem servers, what's the difference between "Running" and "Connected" status in MuleSoft Anypoint Runtime Manager?

The list of all possible statuses for a single server are:

• CREATED: The server was registered to the Runtime Manager console, but never connected.
• RUNNING: The server is up and running, and accepting requests from the Runtime Manager.
• CONNECTED: The server is connected to the Runtime Manager, but is not ready to operate.
• DISCONNECTED: The server was once connected, but now is disconnected.

For reference for all statuses of components in ARM refer to : ARM Rest API 

Usually, when a server remains as 'CONNECTED' for an extended period of time it means that there is connectivity between the server and ARM but the runtimes encountered issues to fully startup. In such case it's suggested to check for mule_ee.log and application logs.
One common issue for a server to remain in such state is an app contained by it having problems when being deployed. In such cases remove the corresponding apps, <APP>-anchor.txt file from <MULE_HOME>/app folder. Docs