Clark's specifies to not eat at all. Kelley's is based on what was done at a clinic in Mass. for quite a while under the direction of doctors, and allows the person doing the flushing to actually eat during the process, and also has provisions for people with a history of gallbladder problems.
I noticed a few people asking whether they could eat during the flush, and this mesage was addressed to them, to give more options, especially to those with a history of gallbladder problems. Thank you for your comment.