What is NYU?

Yes, I know it stands for New York University. However, when I was reading about the application essay, I realized you can only apply once for every major.
Then I went to check the majors and programs.
Here is a example of the Education and Health-Related Fields. http://www.nyu.edu/admissions/undergraduate-admissions/majors-and-programs/education-and-health-related-fields.html
When clicking on Education and Human Development , I see all the fields of the major. That much is fine, however next to the fields it says different school names. Such as College of Arts and Science, NYU Shanghai, Steinshardt, etc.
So does this mean if I apply for “NYU” I am actually applying to another college depending on the major/field?

NYU is a university that consists of many colleges and schools. This is true of all universities.