File Formats
JFIF, by C-Cube, is a minimal file format for simple file interchange of JPEG bitstreams across operating systems and hardware platforms. Adds information about things like aspect ratios that aren’t specified by JPEG. [1]

TIFF, by Aldus Corporation, is a widely used image file format that supports JPEG baseline and Huffman lossless coding.

The closest thing we have to a standard JPEG file format is some work that's been coordinated by people at C-Cube Microsystems. They have defined two JPEG-based file formats:

JFIF has emerged as the de-facto standard on Internet, and is what is most commonly meant by "a JPEG file". Most JFIF readers are also capable of handling some not-quite-JFIF-legal variant formats.

The TIFF 6.0 spec for incorporating JPEG is not widely implemented, partly because it has some serious design flaws. A revised TIFF/JPEG design is now described by TIFF Technical Note #2; this design will be the one used in TIFF 7.0. New implementations of TIFF should use the Tech Note's design for embedding JPEG, not the TIFF 6.0 design.

News flash: the ISO JPEG committee seems to have won their turf wars. They have defined a complete file format spec called SPIFF in the new "Part 3" extensions to the JPEG standard. It's pretty late in the game though, so whether this will have much impact on real-world files remains to be seen. SPIFF is upward compatible with JFIF, so if it does get widely adopted, most users probably won't even notice. [1]