America’s conversation place for mineral owners
I think you are not going to get answers to this question because while people know what executive rights are, it's a common O&G term, "exclusive" rights is going to need definition that will be provided in the body of the document...and we don't have the document. We will need to see the document, if you can attach it. If you just try to describe the context of exclusive to us, I wouldn't put a great deal of faith in any answer you receive.
Off the cuff, with the usual definition of exclusive, If I had exclusive rights to minerals, I would say that I, and I alone would have the right to produce, lease, sell, receive bonus and royalty, borrow money against the minerals and so on. Nobody outside of taking me to court for some demonstrably valid reason could intervene between me and the minerals. My exclusive rights would mean that all others were Excluded, unless I invited them in such as in a lease.
If someone is trying to get you to sign something granting exclusive rights vs. executive rights, don't sign it because you would be gifting/selling the minerals, in my opinion.
Not an attorney, and not in Illinois, but I agree with Mr Kennedy below. You might find something in the Illinois legal codes, but if you are dealing with large amounts, find an Illinois attorney who knows real estate and oil and gas.