Because legally - they are different.
Yes, but the principle involved applies, at least for now, to businesses as well. Schools and employers are addressed in the code itself. While nothing in the law states a business can ask for a doctor's note or other proof, nothing in the law prevents them from doing so, either. Most of what is codified for businesses is physical access. But that said, and you and I have both addressed this, is that there must be some level of disclosure in order for a person to be accomodated, otherwise how can a business make the required accomodation.