For the record, I’m not American nor live in the US, but I have a 19-year-old son who started attending the University of Chicago this year, studying economics. Just the tuition itself is $70k. My husband and I are lucky enough to be able to afford it - I still believe it’s an outrageous amount of money to attend college.
The University of Chicago is private. The University of Illinois Chicago is public. They have the added issue the people definitely use the names interchangeably because they don’t know there’s more than one.
When I worked at the state University, we had lists to check that stuff. Sometimes it’s obvious, other times, not so much. Good catch!