I looked at the page How do I view Assignments as a student? and see the following criteria for an Overdue assignment:

• assignments and discussions that are past the due date, are still available, have not been submitted, and have not been graded.

The difference is that Overdue is only available for assignment and discussions. Note the mention of quizzes in the definition for Past Assignments:

• assignments and discussions that are past the due date and either are not available, have been submitted, or have received a grade; quizzes that are past the due date.

It looks like New Quizzes aren't treated any differently than Classic Quizzes for this purpose.

Thanks @zabeljonathon for your question. I wasn't familiar with the options that students have for viewing the Assignments page (I keep it hidden), and now I know!