My example was probably s*** but the two things are different. It sounds like you've already made up your mind but I'll try again anyway.
Here are the definitions as I understand them, which are just copied from BP. Control is the ability to simply keep the ball within the strike zone, though not necessarily within any particular location of the strike zone. Command is the ability to precisely locate pitches, in or out of the zone, with the goal of keeping each pitch out of the heart of the plate.
Where you're wrong IMO is when you say "They literally say that the ability to put the baseball in the strike zone is different from the ability to put the baseball on the corners, as if it is possible to be bad at one of the two skills but great at the other." It's easily possible and quite common but probably only one way and that way is having control and not command. It's hard to provide examples because there aren't really stats for it. Baseball Info Solutions keeps track of command but I don't have access to it.
TL;DR. Think of it as control being a good skill to have but command being a better, more specific and encompassing skill. Basic logic (to borrow your term) is that being able to throw the ball over the plate is good and takes some skill, but pinpointing the baseball is kind of hard and takes greater skill.