[The Champ]

The section width is the widest area of the tire - the sidewall "bulge".

The tread width is most important to contact as the wheel turns if the tread area is the culprit of any tire rubs.

The sidewall "bulge" is more of a concern with possible contact with the fender lip as the tire moves up and down due to the road surface and also for contact with frame rails or other suspension components on the inside.

I understand your problem with the disc brakes - I personally went through this. My 235/60/15's that I used to run on my car were fine before the conversion. After the conversion, I would get a rub in certain situations. That's why when I went with my 17's - I added 3/8's of an inch BS to alleviate my problem.