I've heard that animals that roar cannot purr, so I don't think the two are related. From what I've read, there is something in the cats brain that signals the laryngeal muscles to contract, which cause the vocal cords to move - something like that! I hope I'm remembering it right!
I've also heard that kittens begin to purr shortly after birth to let their mother know that they are ok, that they are well and content. AND, they cats and kittens purr as they inhale or exhale, unlike meowing which happens only on an exhale.
One of our cats purrs so loud you can hear her across the room! :)
One more fun fact I learned once when I looked into it... racoons can also purr! :)