There are options for saving TIFFs as compressed files, but in most cases, this is lossless compression. Your compressed TIFFs will be smaller than uncompressed TIFFs but larger (probably much larger) than JPEGs. One of the options in some programs is to save a TIFF using JPEG compression; this is lossy. All other common TIFF compression options are lossless.
TIFF compression is only somewhat widely supported. Most TIFF implementations support LZW compression. Many do not support other compression options, so if you save your TIFF using the ZIP compression option, for instance, don't be surprised if a different program can't read it, or if your local lab, which says it can handle TIFFs, can't read your files. Uncompressed TIFF is a pretty safe option for compatibility.