Same company, I think?
I went to a Hardees and saw some deserts with the words "Carl Jr" on them. I had no idea what that meant until I read your post.
Hardees bought out "Burger Shef" in St. Louis over a decade ago. All the "Burger Shefs" became Hardees.
Sort of like Shoney's, the own those "Big Boy" stores and "Captain D's Seafood", "Lee's Famous Chicken", and some others. You wouldn't know it unless you worked at one (like I did over a decade ago when I was in college) or know somebody who works there or own stock in the company.
"In order to completely solve a problem, you must make sure that the root of the problem is completely removed! If you leave the root, the problem will come back later to get you." - Norman King