I get it, but I don't feel comfortable putting my car in the hands of an Arduino.
Nothing against the open source software at all. It's the fact that the Arduino is a consumer experimentation board, not an automotive rated component. I'm concerned for the reliability of the Arduino under the operating conditions of an automobile.
Android auto is your phone projecting to your cars infotainment system. This can work independent of what the cars operating system is.
Android automotive is Android "optimized" as an operating system for a cars infotainment system.
Android auto runs on your phone.
Android automotive runs in your car.
Android auto runs on your phone. Android automotive runs in your car.
Yes, but Android Auto does need some work on the car OS side to operate, i.e. within Android Automotive in this example (although Blackberry QNX is probably more common these days, automakers are moving away from it)