There are a lot of flavors of MPEG (1 2, 1 Part2, 4, etc). Motion JPEG compresses each
frame separately, giving you 24, 25, 30 (for example) distinct frames per second, while
MPEG looks at a number of frames together and, depending on which MPEG, compresses
groups of frames together so they're interconnected, which is what made editing MPEG
difficult until recently.
As well, the two are not compatible with each other and are based on standards set by two different groups. Motion JPEG is most often used for interlaced sources, while Photo JPEG is for progressive. The JPEG formats use all I-frames. MPEG can use either all I-frames, I and P frames, or I B and P frames. Generally, by using IBP frames for an MPEG encode, you can compress to a much lower bit rate while retaining core quality. Because JPEG can't use IBP however, there is a certain threshold that is much higher than MPEG where quality significantly drops. The flip of this is what Ed noted however, in that editing MPEG is not as easy or convenient as MJPEG.