What's a Wiki?

Not a particularly hard question, and most people (whose primary exposure to the term is through Wikipedia), will pipe up: It's a website that lets anyone edit and make changes. And they'd be right, but there's more to it.

A Wiki was originally designed around the philosophy of incompleteness and interaction. The concept, created by Ward Cunningham was intended to foster collaboration [which] creates and develops new ideas.

But it's extremely difficult to know just exactly how your idea will be adapted and ultimately play out when presented to the world.

Wikipedia came along and decided to classify content using a Wiki, becoming the world's first collaborative encyclopedia. And it has stayed true to the ideas above. It's both incomplete and promotes interaction. But it doesn't use Wiki technology to develop new ideas. That's not why it was created.

Is Wikipedia any less a Wiki, then? Not really. While the original intention of Wiki may have been to foster the creation of new ideas, the functionality it provides to do that (i.e. ease-of-use, simple markup, natural collaboration) lends itself to other goals as well.

So then, a Wiki may be:

Content Creation Wiki
The original intention of a Wiki -- to collaborate and create new ideas. From c2.com:

Treat a page here as a half-finished piece of sidewalk art. Don't scuff it up. Don't rub it out. Don't write messages on it like "finish this you bum or I will scuff it" or "I disagree" or "me too".

Instead, see if you can head it toward completeness. If you can't do that now, leave it be. Maybe one day you will think of something to add. Or perhaps another will. We rely on each other to help new things come into being, like ants building nests.

Content Classification Wiki
Sites like Wikipedia, which classify existing knowledge to make it usable. These sites tend to be larger, edited more stringently, and try to present knowledge "authoritatively". [link]

Knowledge Base Wiki
I'm adding this one, since I'm increasingly seeing Wikis used this way. This type tends to be specific to organizations, and are either used to accumulate and distribute information about a specific product or service, or used internally to collaborate and share information, e.g. company policies, inter-departmental information, etc.

These Wiki "types" really only differ in their intention and audience. They all foster collaboration, are simple to use, and are generally ongoing, with no real finalization date.