It is not that TIFF cannot store more data than RAW, or that TIFF files are not bigger than RAW files - it is that digital cameras do internal processing on the image before storing it in either TIFF or JPG format, so data is lost. RAW is essentially unprocessed, the camera does minimal 'work' on the image before storing it.
A classic example of this is white balance. With either TIFF or JPG, white balance information is chosen by the camera, and encoded in the file. You have very limited options to change white balance in post-processing. RAW is encoded before the camera chooses white balance, so all of the potential data is present, so that in post-processing, you or your RAW post-processing software must choose the correct white balance - but there is much more data present, and much more room to maneuver.
http://photo.net/learn/raw/
http://www.ronbigelow.com/articles/raw/raw.htm
TIFF is a better choice than JPG if your camera offers it, unless file size or speed of writing to the card is a primary concern. Otherwise, RAW is technically superior to both.