I'm thinking of buying the Spore Creature Creator, and I'm wondering if it has all the editors/parts of the full Spore game?
The Creature Creator was released as a quasi-demo shortly before the actual game. Even though it is something you have to pay for, it was released with the intention of users buying it to play with while they waited for the final game - with most stores offering rebates on the purchase price of this "demo". While it contains many of the options for body parts found in the full retail version, it lacks many others.
Additionally, the added parts that can be found in the "Creepy and Cute" expansion pack are not compatible with the Creature Creator.
I would strongly suggest buying the full version, as it's very often on sale, over the Creature Creator.
The creature creator was created to create some "initial" creatures to be available in Spore when it launched. Maxis could only create a handful of creatures to begin with, and they needed several thousand more creatures for what they envisioned of the typical Spore play experience.
It served as a demo of the main feature of Spore, editing creatures, as a revenue stream (the free demo hooked people to buy Creature Creator, giving them access to more parts), and as a way to keep the Spore hype going.
Initially, the purchased version of the Creature Creator included all the base parts available in the full game of Spore. However, Maxis then went and released free bonus content for Spore (which isn't available in Creature Creator), and then the Spore Parts expansion "Creepy and Cute" parts pack. So the Creature Creator no longer has all the possible parts of the full game.
All creatures, buildings, and vehicles are stored as a png file locally on your machine. This includes creatures made in the Creature Creator. In addition to the local copy, you can create an account on the Spore server(s). This allows you to "share" your creations online. These shared creations can be viewed on the Spore website, and will be available for download to all players of Spore that allow the game to pull content from the Spore servers.