Functional testing deals with checking the functionality of a system or application works as expected. You give certain inputs and check whether you get the expected output. You will usually use some sort of heuristic to tell whether result is expected or not.
Non Functional testing deals with checking the non-functional aspects of systems such as performance, reliability, scalability, usability etc.
Accessibility testing is about evaluating how accessible/usable a product is to people who have Motor, Cognitive, Visual or Hearing impairments to some extent. To ensure an application is accessible the UI design is really important. Also the application should compatible with accessibility standards set forth by Web Content Accessibility Guidelines 2.0 which include things beyond just the UI.
So, I would say that accessibility testing cuts across both functional and non-functional testing.