V = IR. It's voltage that causes the current to flow.
You can certainly get a lethal shock from a car battery if you pierce the skin with an electrode attached to one of the terminals, due to the reduced resistance through the body, but you're not going to get one through your skin.
The amount of current required to stop you breathing is as low as a few hundred mA, and only 1A to stop your heart in v-fib.
On the other hand, even wet or broken skin should offer about 1 kilohm; so your chances of being electrocuted by a car battery are slight.
I believe that AC is way more dangerous than DC, and particulary the low frequency (50-60 Hz) that are used on normal mains, once upon a time lighting in tunnels (during excavation) was through a frequency converter that elevated frequency (i.e. essentially making AC more similar to DC):
A DC shock may stop the heart (which once the contact is broken is easier to restart) whilst AC males it fibrillate, and there is the "tetanic" reaction induced by AC that in many case might make the contact last longer or be impossible to break.
The old, basic rule is - in case of doubt if a wire is live - to touch it first with the back of a finger, and never with a fingertip, as the reaction to the shock would be to close the finger/hand around the wire in a very tight grip.
It is usually voltage that kills you, but not all electric shocks are equal. The type that kills you quickly is one that goes through the heart, disrupting its rhythm. This happens, for example, if you use both hands to work on something electrical. It doesn't need much current at all. Electricians are trained to not use both hands. If you use only one hand the shock is more likely to be straight to ground. In that case a high current is going to do more damage to you, but might not actually kill you. But in any case you need enough voltage to overcome the resistance of the skin the first place.
At such a low voltage, and a DC voltage nonetheless (so you're only dealing with resistance, and not impedance), you will never get enough current through you, even if you'd just waded out of the ocean.
