One's a right and the other is a privilege.
That's answer #1 (maybe 2 and 3 as well?).
The answer after that is: a car is more complicated, has more moving parts & controls, and can result in greater injury or loss of life in an accident than a gun. Unless you are purposefully shooting up a mall, the negligent discharge will usually be limited to one victim (injured or killed). A pickup truck or SUV can kill a whole bus full of kids in a single accident. Risk of dying in a vehicle crash is MUCH higher than dying from a gunshot, whether accidental or intentional.
Think about all the traffic laws and rules you have to learn. Traffic signs you must obey and what they mean, what to do if an emergency vehicle is behind you, how to proceed at a 4-way stop without a signal, when it's legal to pass another car, etc., etc.
There are a few basic safety rules for guns. Follow those, and everything else is practice and cleaning! Driving requires a license because the knowledge and skills needed to be safe necessitate a driver have appropriate training and hands-on experience. Using a gun is much safer statistically than driving.
There are states which issue CCW licenses that require proficiency testing with the firearm you intend to use. I'm okay with that. I don't want someone who never practices drawing down on a bad guy with me in the same room!!! But, for controlled situations like hunting or target shooting, no license is necessary to be safe.