Can Hubitat distinguish between a Caseta dimmer being turned on physically vs. digitally?
The two events are distinguished in the event logs.
Depends. It will do this very well, if Hubitat is the only hub connected to the Caseta Pro Bridge via a telnet connection. And as long as you are not using automations on the Lutron app itself.
Basically, Hubitat monitors the telnet stream. If hubitat itself sends a command to control the dimmer, that is interpreted as a "digital" event. OTOH, if there is a change in dimmer status observed in the telnet stream that was not requested by Hubitat, it will be interpreted as a "physical" event.
Note that this physical event could have emanated from an automation in the Lutron app, or from some other hub connected to the Caseta bridge via telnet.
As @aaiyar noted, it is possible to define automations within the Lutron app. If you do so, it may prevent Hubitat from tracking the automations, although Hubitat will be able to see the results of the automations.
I suggest doing all your automations within Hubitat apps. That makes it easier to troubleshoot problems.