The difference is that the DNG file is nothing more than a raw file that is inside a wrapper. This simply means that when you export it to another program, the receiving program will treat it like the raw data file that it is. Colour space will not have been assigned nor will the white balance have been "baked in" nor with image bit depth be assigned. These value can be changed by the upstream raw converter without any issues that affect image quality. Gamma is also technically variable, but pretty well all computers and editing software use a 2.2 value, so this is not of great importance.
The TIFF is an image file, so color temperature, colour space, bit depth and gamma will all be "baked in". Sometimes these can be changed (colour temperature cannot), but there can be quality consequences. TIFF files support layers and support lossless compression. Photoshop PSD files are little more than a proprietary TIFF file with a few bells and whistles. TIFF files tend to be fairly large...