Not necessarily.  Although most colleges must comply with Section 504 and the ADA, there are several differences in eligibility and services that a student may receive.  It is important to be aware that the bulk of responsibility is on the student at the college level, so self-advocacy is an important skill for your child to learn before he/she leaves high school.  Attending his/her 504 meetings while in high school is a good way to learn that skill.  One difference is in what is called "child find".  Public schools are required to locate and identify students who have disabilities.  In contrast, at the college level, students with disabilities are required to approach the college to request accommodations.  In addition, any testing required to substantiate the disability must be provided by the student at the student's expense.  After receiving notification of disability, the college reviews any information provided and determines what accommodations the student will receive.  Accommodations are usually less extensive than those on a high school Section 504 plan.