You are correct on both modes of transport. Either...
1) Unloaded, cased, and inaccessible by passengers, or
2) Can be loaded, but must NOT be concealed which means in plain sight.
I called the NSP years ago when I got my first handgun and asked that question. The officer I spoke to suggested that if you get stopped, to place the pistol on the dash. However, I would make sure this is done well before the officer walks up to the vehicle. Personally, I think having it in plane sight could cause more complications than it is worth.
Fly