What is the difference? Is it just burn factor, or do they have different light scattering/diffusing characteristics?

almost all gels or diffusion have the same heat capibility. there are some gels that manufactures make for different uses.. aka, still vs Cinema and sometimes there is cross over when one gel is the same in both swatch books but listed by a different number. Most of the time diffusion is a matter of experimentation and personal preference. Once you settle of a type or brand you like you may be unlikly to change. i have seen people get very depressed when a diffusion is discontinue. I hope this helps. If I find my swatch I will tell you more. GAM and Rosco also make gels

Tough spun is very thick, not particularly efficient. Pretty much old school. Occasionally it comes up as a punchline on set.

The Lee 3 are 216, 250 and 251 which diminish in opacity as listed (and thus increase in transmission). Rosco's rough equivalent are tough frost, half frost and opal.

I agree with what has been said so far. The word "tough" usually means heat resistant and "Soft" isn't. Tough can be pinned on barn doors and put in gel frames in the light. Soft can't it needs to be in a frame away from the instrument
Spun is old school, and I guess I am too. It comes in different weights/thickness, 1/2, 1/4 and full. It was a long time ago but it was actually spun fiber glass. You could buy rolls of it and cut pieces then pull it apart and get the thickness that you wanted.
I try to keep a variety of diffusion, both spun and frost in my kit. I beleive that there is a difference in the light and I use different material with different instruments depending on what I want.