Q: Can someone please explain the difference between FLIs and FLCs, and how I can convert between them, and how I can compress either to get an optimum size.

A: The difference is small:

FLI was introduced with the Autodesk Animator 1.0 It supports only one resolution: 320x200 with 256 colors

FLC was introduced with the Autodesk Animator Pro It supports any resolution up to 1024x768 with 256 colors.

(Just for your information: the FLI file created by AA Pro cannot be used in AA 1.0. 3DS writes the FLI as AA 1.0 compatible, but can also read the FLI from AA Pro.)

The compression is lossless and cannot be controlled. Generally, the Flic format saves the first frame as a whole image, and every next image as the difference (delta) to the frame before. This means that you will get a VERY HIGH compression if only a small part of the screen changes (like a ball rolling through the scene), but if you move the camera around, almost the whole frame has to be written.
Also, if you repeat the same frame 100 times, only an index is written to tell the player to repeat the one frame 100 times. The lenght of a 1 frame and a 100 frame animation in this case would be almost the same.

The Flic itself can be compressed with PKZIP at about 40%, which shows that it is not as compact as a GIF (0,1%). There is a utility called Smacker that compresses flics (with a lossy, but very high quality compression) to save space (best for games!)
(see http://www.radgametools.com)