What if TheBrain had two different check controls: checkboxes and checkcircles?

☐ Checkbox = Todo - Works as it does now and appears in TheBrain's Todo list.

◯ Checkcircle = non-Todo - You can check and uncheck it just like a checkbox, but it never appears in the Todo list.

Sometimes a checkable item isn't something you need to do. It might represent a status, condition, or progress. For example:

☐ Contact vendor about outstanding check
◯ Check has cleared the vendor's bank

Or you might have a list of book chapters that you want to check off as you read them without turning every chapter into a Todo.

The different shapes would make the distinction immediately visible:
Square = action
Circle = status/progress

So, if a square you put a check in is a checkbox, it seems only logical that a circle you put a check in should be a checkcircle.