What can you do in "Sound on Sound" mode that you MUST NOT DO in "Comping" mode?
For instance: 
Comping mode - Can you split a take in a lane into many parts and move them into different positions within that lane?
                         Can you save all your takes as separate wave files and use them in a different song as regular tracks?
 
What are the "rules" that define the differences between the two editing modes?  The first one above is the main concern for me.

I really never use sound on sound. You can do anything with comping.

Sound on Sound is like overdubbing on a tape. Comping is better for multiple takes then splicing out the best parts before consolidating them to a single track.
 

For the first part of your question, yes, you can split and move around, I've done it with guitar fills/licks/solos. The second part, I'm not sure of as I've never tried. 

Comping and Sound on Sound are not so much a distinction in editing but more on what happens when you record multiple times over the same time area.
 
In comping mode the previous audio is muted and the new take becomes what is audible. Each take is saved in a take lane that can later be "comped" taking parts from each take as desired.
 
In sound on sound mode the only difference is that each take is audible. That is, if you recorded a part 4 times you would have 4 takes in 4 take lanes and they would all be playing.  If you open the take lanes you can comp, edit and mute areas just as if you had recorded it in comping mode.
 
In overwrite mode each take overwrites the previous data so you only end up with one take.
 
That is my understanding at least.

reginaldStjohn
Comping and Sound on Sound are not so much a distinction in editing but more on what happens when you record multiple times over the same time area.
 
In comping mode the previous audio is muted and the new take becomes what is audible. Each take is saved in a take lane that can later be "comped" taking parts from each take as desired.
 
In sound on sound mode the only difference is that each take is audible. That is, if you recorded a part 4 times you would have 4 takes in 4 take lanes and they would all be playing.  If you open the take lanes you can comp, edit and mute areas just as if you had recorded it in comping mode.
 
In overwrite mode each take overwrites the previous data so you only end up with one take.
 
That is my understanding at least.

That's about right...    Comping, Overwrite and Sound on Sound are classified as recording modes.  
http://www.cakewalk.com/Documentation?product=SONAR&language=3&help=Recording.10.html
 
What you do with the clips after the fact, that's the editing side of comping (or layering where applicable).

Just to note, these modes also apply to MIDI recording. Sound on sound is useful for doing things like building up a drum track by looping and recording each part (kick, snare, hat, etc.) during multiple passes.

Even when running with "Sound on Sound" the take-lanes are used. However, they are not expanded, and it's simple to bounce everything into one track. This is how I make my percussion tracks.