Once friend made few photos for me. Park, people have rest. Friend gave me photos. Every photo was in two formats - TIFF and CR2.
TIFFs I use for editing, storage. From TIFFs I make JPEGs for blog.
What are the benefits of CR2?
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The CR2 format is the Canon raw sensor data as opposed to an image. It is losslessly compressed. Some newer Canon cameras support CR3 format which can be compressed in a very slightly lossy manner.
I suspect the TIFF files were created from the CR2 files. Usually, cameras cannot store the pictures as TIFF; they can store as JPEG (heavily lossily compressed) or RAW (usually losslessly and sometimes very slightly lossily compressed).
The TIFF file is one interpretation of the sensor data as an image. It has some demosaicing algorithm to convert the brightness values of the sensor behind the Bayer filter to colors of individual pixels. It has some denoising algorithm. It has some white balance settings. It has some exposure correction. It has some lens corrections. Most likely the photographer fine-tuned the settings to give the best possible image.
If you want to do the fine-tuning yourself, you need to open the CR2 files in an application such as Lightroom, Darktable, RawTherapee or Canon Digital Photo Professional. With the CR2 files, it is possible to e.g. change the white balance or exposure correction.
You may even find that over time, as computers become more powerful, they can better interpret the raw sensor data to form an image. An example of this is Digital Lens Optimizer which is now available in Canon Digital Photo Professional. You can use it for RAW files shot before the Digital Lens Optimizer was available. But for JPEGs you cannot use it.