With S Scale track the "S" designation seems to be used only by AM and it refers to the diameter. So 24 inch radius AM track is also known as S-48 on their website.
For Lionel (American Flyer) in their current catalog they use the letter "R" to indicate radius and MTH (S Scale S-Trax) on their website simply spells out the word "radius." No "S" is used in either case.