Alot of car companies have their own financing options for example;
Ford Motor Credit
Toyota Financial Services
Im not sure who they are ALL backed by but when you buy a car your paying back the financial institution. Once you
sign the papers for a loan any down payment money goes to the dealer itself then they get the money for the cars value
from the bank. Once you purchase the car you will call the insurance company and give them all the information to add the
car to your insurance. Insurance company will ask if you lease, finance or own the car outright.
The way it works is that the auto manufacturers and dealers have correspondent accounting relationships with banking institutions whereas if you do "dealer financing" it's still financed by a bank but the dealer and auto manufacturer take a cut off the interest. Regardless of where you go you'll be financed by a bank. The difference is that banks give auto manufacturers discounts on their rates since they send them so much business which is typically why the dealer financing is sometimes at a lower rate. This isn't the case of all auto manufacturers as some auto manufacturers have their own financing arm which in and of itself is essentially a banking institution which allows them to set their own rates.
To answer your questions at the end tho. If a loan is taken out to purchase a vehicle the bank will have a lien on the vehicle as far as insurance in concerned. This differs if you take out an unsecured loan or pay for a vehicle out of a heloc or something of that sort since in those instances you are essentially buying the vehicle in cash and as such you are the only owner of the vehicle.