In general yes you can make that distinction but more importantly this is a problem for peace time.

No one would authorize a non-visual shoot down of a target in a non-active AO and not during an actual conflict.

If you are at the stage where you have factions duking it out in the skies especially these days were talking about a major conflict in which case there won’t be any civilian jets flying there anyhow.

There is probably a way they know his, but can you really fire a missile at something on a computer screen miles away and be fully confident the thing you are shooting at is enemy military aircraft? And not say a civilian aircraft ?

I guess if its going fast enough its almost certianly a military aircraft. Can the radars in the military jets identity the type of the aircraft before it gets blown out of the sky?

Radars on the F-15 can determine the type of turbine on an aircraft...

Another way is to announce a no-fly zone and then assume anything within the zone is hostile. (Yes, civilian planes can still fly there, but they've literally been warned at that point)

I assume this would happen pretty quickly when a war went hot.

That lets you distinguish friend from not-friend, but not enemy from airliner.

Until it isn't, because the enemy has already captured and compromised your government back home.