As you noted insurance company guidelines and policy terms can differ but in general your auto insurance liability policy would normally cover another person driving your car if you gave them permission to do so.
Typically insurance follows a car primarily and the driver secondary. This means that the vehicle's owner's insurance is used first if a friend drives their car and has an accident. If the damages sustained by those placing claims against your liability coverages go over your limits then the driver's insurance would be used next for excess.
There can be exclusions due to age, etc as part of an insurance policy so to find out for certain if your auto's liability insurance will cover you loaning your car out to your friend, check with your insurance agent.
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