AFAIK a 0-day exploit is an exploit that was found in the wild. No one previously knew about it and there's a scramble to fix it.

In a week this exploit will be an "old 0-day exploit" because the "0-day" bit describes developer preparedness at discovery, not how long the exploit has been known.

"n-day" refers to the number of days since a fix was released. So a vulnerability can be "0-day" indefinitely if the software maker never patches it - and in those circumstances it would make sense to talk about an "old 0-day".