Level AA is a little more significant, and makes sites accessible to people with a wider range of disabilities, including the most common barriers to use. It won't impact the look and feel of the site as much as Level AAA compliance, though it does include guidance on color contrast and error identification. Most businesses should be aiming for Level AA conformity, and it appears to reflect the level of accessibility the DOJ expects.
The ADA is the Americans with Disabilities Act, passed almost 30 years ago in 1990. This act was originally put in motion pertaining solely to physical location. It requires establishments to provide people with disabilities easy access to various levels throughout the business. This act was set to achieve an equal experience to all people, handicapped or not.