They are both compressed formats. TIFF files are around one-third the size of the uncompressed image. JPEG files can be compressed at varying rates. Many digital cameras will have several compression or quality settings. They may also combine a choice of compression and resolution.
Most digital cameras come with software to edit and manage the image files created by the camera.
The quality and usefulness of this software should be one of the factors you consider before making a purchasing decision. We have only scratched the surface and there are several other factors that should be mentioned. Camera image storage is a major consideration. Digital cameras store their captured images in internal memory or on some type of removable media. If the camera stores it's images internally and the memory becomes full you must either delete some of the images to make room, or connect the camera to a computer and transfer the files.