What is an affiliate professor?
In the example you give (https://grainger.illinois.edu/about/directory/faculty/ghmiley), the person is &quot;professor emeritus&quot; in one department, and &quot;department affiliate emeritus&quot; in another.
I can't speak to that university in particular, but in certain universities, a professor in a given department can only take on graduate students from that department.  Affiliate status with another department allows a professor to take on students graduate students from that department as well.