RAW to TIFF or PSD 16bit loses color depth

I was under the impression 16 bits would keep the same depth. But for my great shock I have noticed that there is a considerable lost of depth.

Testing with a Canon Mark II raw and using both Lightroom and Camera Raw exporting to TIFF or PSD 16bit. And yes, I know how to set camera raw to produce 16bits instead 8

Notice how with RAW the Sun is kept when reducing exposure with Photoshop but is lost with TIFF. If fades directly to a bland dark grey without any sun shape detail.

Include the link to the original RAW and the TIF in case anyone wants to check. And if you want to reproduce the problem simply load it in photoshop (or lightroom) and save it as 16 bits TIF. https://www.dropbox.com/sh/arsg3eem4dllc0m/AACM-Mdqy_8BNw8GjPJ6dEvma?dl=0

I add more examples to explain my point that there is a evident degradation of data. About that the sun is overexposed, I talk about dynamic range lost compared with the original RAW as shown in the example. This is part of a multi bracketed series of photos and I have other exposures. You cannot capture the full range of the sun with a single exposure. Example with RAW: Example with RAW moved to Photoshop and abandon camera raw, in 16 bits, 0-1-2-3:

Now I convert it to 8 bits to see the difference. Again 0,-1,-2,-3 exposure. And the results are identical to the 16 bits no RAW. And this certainly should not happen. Again you have the original RAW file in my link if you want to double check.

It would be less of a problem if I would not get same results in Lightroom and camera raw, leaving me with no alternatives. I hope everybody will agree 8 bits and 16bits should not look so similar, unless there is something wrong here.