If a security bug is exploited in the wild, it's an n-day if it's been first exploited n days after the publication of the bug, and a zero-day if it's been exploited before or on the day of the publication.
When a bug is not yet exploited in the wild, it's just a discovery of a bug, not a zero-day.
Does "publication" refer to the software or to something documenting the existence of the bug? Because I thought zero-day meant the bug was exploited the same day the software containing the bug was released, but your phrasing sounds like if you exploit a bug before the maintainers know about it then it's a negative day.
If a security bug is exploited in the wild, it's an n-day if it's been first exploited n days after the publication of the bug, and a zero-day if it's been exploited before or on the day of the publication.
When a bug is not yet exploited in the wild, it's just a discovery of a bug, not a zero-day.