As was stated in section 1, JPEG is only for still images.  Nonetheless,
you will frequently see references to "motion JPEG" or "M-JPEG" for video.
*There is no such standard*.  Various vendors have applied JPEG to
individual frames of a video sequence, and have called the result "M-JPEG".
Unfortunately, in the absence of any recognized standard, they've each done
it differently.  The resulting files are usually not compatible across
different vendors.

MPEG is the recognized standard for motion picture compression.  It uses
many of the same techniques as JPEG, but adds inter-frame compression to
exploit the similarities that usually exist between successive frames.
Because of this, MPEG typically compresses a video sequence by about a
factor of three more than "M-JPEG" methods can for similar quality.
The disadvantages of MPEG are (1) it requires far more computation to
generate the compressed sequence (since detecting visual similarities is
hard for a computer), and (2) it's difficult to edit an MPEG sequence on a
frame-by-frame basis (since each frame is intimately tied to the ones around
it).  This latter problem has made "M-JPEG" methods rather popular for video
editing products.

It's a shame that there isn't a recognized M-JPEG standard.  But there
isn't, so if you buy a product identified as "M-JPEG", be aware that you
are probably locking yourself into that one vendor.

Recently, both Microsoft and Apple have started pushing (different :-()
"standard" M-JPEG formats.  It remains to be seen whether either of these
efforts will have much impact on the current chaos.  Both companies were
spectacularly unsuccessful in getting anyone else to adopt their ideas about
still-image JPEG file formats, so I wouldn't assume that anything good will
happen this time either...

See the MPEG FAQ for more information about MPEG.