Your regular car battery is probably https://en.wikipedia.org/wiki/Lead%E2%80%93acid_battery which is a different technology. The Prius uses Nickel–metal hydride batteries. Again, different technology.

The Leaf and Tesla both use lithium-ion. I don't know why the apparent difference. But per https://www.tesla.com/support/vehicle-warranty-m3, Tesla's battery warranty is 8 year or 120k miles, and comes into effect if your range drops by 30%. So they expect better performance than the apparent real world performance of the Leaf.

I also do not know why there would be a difference in those technologies.