When a camera takes a digital photograph the image produced internally within the camera is in what's know as camera raw.
Camera Raw: A camera raw file is effectively a digital negative of the photograph taken. All professional level camera will allow this raw unprocessed image to the be saved directly to the cameras storage for later processing, hence being referred to as camera raw. This format varies between camera models and camera manufacturers. Much of the better image processing programs such as Adobe Lightroom, Adobe Photoshop, Affinity Photo, Capture One and DxoPhoto Lab all offer the ability to process these camera raw files and produce final images for use.
This is the best format for use when storing images (particulary for later processing). Since the image has not already been processed it is possible to leverage the better processing power and in some case advances in software which have occured since your camera was manufactured. This will always produce a superior result for an increase in the file size generated.
The range of adjustments that can be made to raw images is much greater allow much greater creative freedom than is possible with a jpeg file.
JPEG files: The JPEG file is a compressed format file which uses lossy compression to store the image. The use of lossy compression means that there is a trade off between size of image stored and image quality.
Where a JPEG file is generated by the camera the user has little (often no) control over the adjsutments made during the files generation. Most cameras will take the original 12 (or higher) bit depth image and reduce it to 8 bits before further adjusting and then compressing the image to store in the JPEG file.
If subsequently you wish to modify the decisions made when the camera processed the image, such as white balance, exposure or colour correction there is only a limited ability to do so. Much of the orignal data generated by the camera is thrown away whilst creating the JPEG file.
TIFF files: A TIFF file is capable of being stored in uncompressed, lossless and lossy files. It is possible to store images in TIFF files using a 16 bit depth which allow all of the orginal tonal values from the camera to be preserved. This makes it the preferred format for storing a fully corrected image before sending it for final ouput (i.e. printing). Lossless compression of TIFF files does require much more storage so it is less suitable for day to day image transfer, but is best used where it's incereased qulity and capability is required.