Most cameras shoot RAW as 12-bit or 14-bit... while a TIFF file is typically 16-bit.
16-bit has about 64 times more possible colors and tonalities than 14-bit (4.39
trillion).
16-bit has more than 4000 times more possible colors and tonalities than 12-bit (68.68
billion).
16-bit has more than 16000 times more possible colors and tonalities than 8-bit (16.78
million).
16-bit images have a color palette of 281
trillion possible colors and tonalities!
When you open the image in post-processing software, it interpolates a 12 or 14-bit image as 16-bit. In a sense it "expands" the tonal information to fill the space.
Only a few cameras shoot 16-bit natively (most I'm aware of are medium format digital).
When you "shoot JPEGs", the camera actually takes a RAW image (all do, initially) and then immediately converts it to an 8-bit JPEG "in camera", using the settings of the camera. Whatever the camera deems "extraneous" is thrown away.
Shooting RAW requires you post-process the image later in software, but gives you opportunity to change a lot of the settings that were noted in, but not applied to the RAW file.
In most cases it's best to post-process and "work" your images in 16-bit mode. While it's possible to convert it to 16-bit, it makes little sense to do so if the image has already been "reduced" to an 8-bit JPEG... much of the data need to work the image in 16-bit mode has already been thrown away.
If you've been working on an image in 16-bit mode and need to close the image, but will want to open and work on it further, best to save as 16-bit TIFF (or PSD, etc.)
Once the work on the image is finished, for most purposes it's fine to save the image as 8-bit JPEG. It's a more common and widely viewable format than 16-bit TIFF or PSD (etc.) 8-bit files are much smaller and more practical for most purposes. And you won't see any difference between 8-bit and 16-bit finished images when viewed on computer screen or in prints made with most processes. 16-bit may not be possible with some printers. Or, if possible, may make printing slower and consume more ink, while not improving the result in any way. But check with your printer... some processes can utilize higher bit depth files.
More info here (and a lot of other places online if you Google it):
https://www.diyphotography.net/8-bit-vs-16-bit-color-depth-use-matters/https://photography.tutsplus.com/articles/bit-depth-explained-in-depth--photo-8514https://laurashoe.com/2011/08/09/8-versus-16-bit-what-does-it-really-mean/