The 16-bits used to record raw data and the 16-bits (per color channel) used to record a demosaiced and gamma corrected TIFF or PSD are not used to represent the same exact thing in the same exact way. Expecting a 16-bit TIFF to be the same as a 16-bit raw file is a bit like expecting a 16-bit WAV audio file to be the same as a 16-bit WMA file. They both contain information about the same sounds, but how much information they contain and the way they represent that info is very different.
In the case of the raw data, the 12/14/16 bit information is of a single linear monochrome luminance value for each pixel well. Effectively what we have with a raw file from a Bayer masked sensor is a B&W photo (but with a linear response - more on that below) using a green filter for 1/2 the sensor's pixels, and blue and red filters respectively for 1/4 of the pixels.
To get color information from a raw file, it must be demosaiced. Again, back to our B&W film analogy, by comparing the differences in brightness of the same areas in three B&W images of the same framing with each filtered respectively for red, green, and blue the three monochrome images can be used to create a color image. That's the way most color astro photographs through the mid to late 20th century were produced. That's the way color film works. It's the way digital sensors work. It's the way our retinas + brains work.
Before we convert raw data to a TIFF, we also usually apply gamma correction (a light curve that converts the linear response in the raw data to a logarithmic response closer to our human perception - again, we use the same words but it is not exactly the same thing as when we apply gamma correction to the signal going to a CRT display). If we demosaic to produce color information and then translate the numerical values from a raw file to the TIFF image format without applying gamma correction, we get something that looks like this:
With gamma correction applied, the same image looks like this (the low-res embedded jpeg preview from the raw file used to generate the TIFF above):
Keep in mind that when you 'open" a raw file on your computer or other device, you're not looking at the pure, unadulterated raw data on your screen. You're not even looking at a downsampled version of all of the information contained in the raw data. Not even close! What you are seeing is either a jpeg preview image generated by the camera and attached to the raw data file when the photo was recorded or you are seeing a similar rendition of the raw data generated by the viewing application. In either case, the raw data has been highly processed to make the information viewable in a way that we expect. That processing must make certain decisions about black point, white point, gamma correction, white balance, etc. When we "view" a raw file we are looking at one of countless possible interpretations of the raw data. That is why we can edit raw files non-destructively. When we move all of the sliders around and click various buttons we are just telling the viewing/conversion application how we want it to reinterpret the data in the raw file.
Once the data in the raw file has been transformed into a demosaiced, gamma corrected TIFF file, the process is irreversible.
TIFF files have all of those processing steps "baked in" to the information they contain. Even though an uncompressed 16-bit TIFF file is much larger than a typical raw file from which it is derived because of the way each stores the data, it does not contain all of the information needed to reverse the transformation and reproduce the same exact data contained in the raw file. There are a near infinite number of differing values in the pixel level data of a raw file that could have been used to produce a particular TIFF. Likewise, there are a near infinite number of TIFF files that can be produced from the data in a raw image file, depending on the decisions made about how the raw data is processed to produce the TIFF.
The advantage of 16-bit TIFFs versus 8-bit TIFFs is the number of steps between the darkest and brightest values for each color channel in the image. These finer steps allow for more additional manipulation before ultimately converting to an 8-bit format without creating artifacts such as banding in areas of tonal gradation.
But just because a 16-bit TIFF has more steps between "0" and "65,535" than a 12-bit (0-4095) or 14-bit (0-16383) raw file has, it does not mean the TIFF file shows the same or greater range in brightness. When the data in a 14-bit raw file was transformed to a TIFF file, the black point could have been selected at a value such as 2048. Any pixel in the raw file with a value lower than 2048 would be assigned a value of 0 in the TIFF. Likewise, if the white point were set at, say, 8,191 then any value in the raw file higher than 8191 would be set at 65,535 and the brightest stop of light in the raw file would be irrevocable lost.
It appears that when you converted your raw file of the sun into a TIFF, your white point was set considerably lower than the maximum value of the raw file. Everything brighter in the raw file than the selected white point has the same value in the TIFF, so no detail is preserved. Reducing the brightness of the TIFF file just results in the highest values being shown as darker shades of gray instead of white, but they will all still be the same shade of gray. The differences between pixels with values higher than the white point used to create the TIFF were discarded when you created the TIFF.
For more about how and why color information is lost when more than one color channel is at full value, please see: Why is it that when the green channel clips, it turns into blue?