You're right about Illinois law making little sense.
Some of the goofy stuff;
During the muzzleloading rifle only season pistols are NOT allowed. But you CAN use your muzzleloading pistol during the late-winter antlerless-only season so long as it meets muzzle energy requirements.
During the muzzleloading rifle only season your smoothbore is NOT legal to hunt deer. But it IS legal during the "firearm" deer season because then it is a shotgun.
Muzzleloading pistols are not allowed even during the firearm season.
As far as small game muzzleloading, you must carefully check the site-specific regs for any state land you want to hunt.
Sometimes it can be difficult to find out the whole truth. For example, the hunter fact sheet for Sand Ridge State Forrest this year did not mention muzzleloading rifles BUT the rule book says they are OK.
Some only allow shotguns. Some allow shotguns or rimfire. Some allow shotguns or muzzleloading rifles. Some allow all of the above. A smoothbore muzzleloader IS a shotgun when loaded with shot.
On private land you can use whatever you like.