Bucky (the Siamese cat from “Get Fuzzy”) uses purring to lure people into getting close enough for him to rip them up - “That’s not purring!” We’ve got a part Siamese cat who likes to purr while she’s playing roughly with teeth and claws - we like to say that while she’s trying to open up our skin.
To address the OP, I agree with everyone else - cat’s have a lot of ways to communicate with us, and purring is only part of it. I wouldn’t call the chirping, meowing, mewling, whining, snarling, growling, trilling, moaning or mooing purring.
What I’ve read is that cats purr when they are not aggressive, and they want to assure someone/something else of this non-aggressiveness. So a cat might purr when it’s in distress, to signal that it doesn’t intend to claw your eyeballs out.
One of our cats will purr when he plays, even if he’s playing rough. This guy purrs SO much that on his first vet visit, the vet couldn’t get him to stop purring long enough to listen to his heart. The vet finally tried putting him in the sink…but Charlie just kept on purring.
Cats can and will also growl, and usually it’s pretty easy to tell that it’s a growl. Here’s a cat showing all kinds of displeasure: http://www.youtube.com/watch?v=qXLxM0u1aJw