The GIF format [Graphic Interchange Format] is a lossless compression
format, meaning that when it compresses an image it doesn't lose any
information -- the resulting picture is exactly as it originally was
(in the other format, like .EPS).

JPEG or JPG is a lossy compression format.  Many programs that convert
to JPG will let you choose the amount of compression that is used.
If you set the compression to 10 (highest quality, lowest compression),
the resulting image is almost exactly what it was to start with.
If you select something down around 5, it will significantly compress
the image size, but it will look really bad.

You're right in the guess about the black & white image being
compressed better by GIF.  On the other hand, photographs are usually
better compressed by JPEG, set to a quality of around 8.  There will
be some loss of information (resolution), but in most cases it is
not visible to the naked eye.  As you lower the quality, the picture
becomes "fuzzier" or "blocky".  See the following site for some more
information and sample images:
http://www.siriusweb.com/tutorials/gifvsjpg/

Bill Mackin