Doing some digging on the Interwebs, it all comes down to purpose and what each one is.

A RAW file is a record of sensor data, all of it.

A TIFF file is a processed image that no longer contains all the RAW data.

Bit depth reflects the tonal range a pixel can reproduce.

Let's say you took a photo of a fairly contrasty, somewhat overexposed scene in RAW, did some post processing, and exported a TIFF that looked pretty good. The photo editor sees the photo, but knows the most important part was in one of the shadow areas. You can't edit the TIFF because you chose a specific tonal range for those shadows, leaving image data behind in the RAW file. Trying to brighten up the shadows in the TIFF yields not much usable at all because a lot of image data was left behind when you decided on the final tonal range in that shadow area when exporting to TIFF.

The RAW file is a different story. The RAW file still has all the image information for that shadow area. It's really quite amazing what kind of quality can be pulled from a RAW file.

Another way to think about this is printing a film negative. If you make a print and burn in an area that actually looks okay in the negative, the final print won't have the detail in the shadow area that the negative has. You wouldn't take a photo of the print and try to recover the shadow area. That information is no longer in the print. You would re-print the negative because it has more tonal range than you chose to put into the final print.

It is important to understand that a RAW file cannot be used for display or production. Most camera manufacturers have their own proprietary RAW format. And RAW files don't look that good unprocessed. They have to be processed and saved into a display format of some kind, and the final format is chosen based on what the final need is i.e. print, video still, web, publishing in a book, or newspaper (they're still around).

There is a difference between compression and processing. All file types that are not RAW imply processing. All files that are not RAW are processed, meaning that it was made to look good for some final medium. During processing, tonal ranges for dark and light areas of the photo were chosen and the data from the RAW file was used to optimize the look of each area using some of the sensor data that best represented the desired look, leaving data to make the area lighter or darker out of the final image as it is no longer needed. The final export of the edited RAW file is either compressed or not compressed depending on the final format chosen for the image.