Tiff files can be saved either with no compression or compression such as Zip or LZW. Zip is usually, but not always, smaller. But unlike jpeg, these compressions are lossless. So when you load or print a compressed tif file, nothing is lost. It just takes less room on your disk.
But nothing's free. Unlike many files, when you Zip a compressed tif file, it's likely to not get further compressed at all.