If a task by the same name exists in more than one tasklist on the same page, checking or unchecking the completion status of one checks or unchecks the status of the other in sync. Basically, tasks by the same name are synchronized on a page, regardless of the tasklist they are in.

I would expect that tasks in a tasklist are supposed to be independent of any tasks in another list. The current workaround that I'm using to deal with this issue is to create separate pages whenever I want more than one tasklist that contains one or more tasks with the same name, which is rather annoying and artificially increases the page count.