The current rating is a maximum current. The current going through your body depends on the voltage applied across it.
Assuming a worst case where you put one hand on each terminal (sending current through your heart) it would take around 10mA to cause powerful muscle contractions that prevent you from letting go. The average hand-to-hand resistance is around 50kOhms (assuming skin is intact).
Doing a bit of mathemagic, you'll find that the 250V source will drive a far higher current through you, making it far more deadly than the 12V battery. Remember, current is determined by the external circuit.
To answer the comment on AC vs DC: AC is generally more dangerous because you have involuntary muscle spasms and can't let go. A high DC voltage is more likely to cause a single contraction and push you away from the source.
Another addition, your skin can actually suffer dielectric breakdown under a sufficiently high voltage. In medical circles, this is called GGWP (ok maybe not). Basically, most of the resistance comes from your skin, once that's gone, it's just conductive salty fluid all the way and that definitely can't be good for you.