Does the VK and the SF class now refer to the car or the driver?

We have in our household 2 cars with two insurances – both separate, however with the same insurance – one runs on me, the other on my girlfriend. We are in the insurance of the other but each as additional driver because we change the vehicles quite well. I wonder just what happens if we have a self-inflicted accident. Let’s assume that I drive against a wall with her car (or vice versa) – that would now be over her vehicle. And what if I drive a strange vehicle? For example, an acquaintance buys a new car and I would like to try it out and then something happens (or I let someone else drive my car). After we have limited the driver circle in the insurance, I can not let anyone drive, even for 1-2km to test the car. Nevertheless, the driver is still liable for damage. ? Would something like this be covered by private liability? Probably there is already this question, but I could not define a unique search term to filter it out in the forum. Therefore, I am grateful for answers.