What are the types of automobile insurance in USA ?

What are the types of automobile insurance in USA ?

I'm doing a research for my course , comparing this service in my country to which in the USA …and more specifically about the private and commercial cars… a claim saying that USA's provisions are strictly applied ..i.e the son driving his father private car is not entitled to any compensation in case an accident is occurred …..because it's not the “son” car..(which at the same time is not going the same way here …as long as the car is insured so anyone drive it is insured ..regardless of the owner of the car…and just there it is the debate point…what do you think about it ?
so ,I'll appreciate if you could feed me with any thoughts any idea any information any links concerning that or even automobile insurance in general…