Hi Mahlon,
All available tags are stored in the Tags table regardless of what table the tag is used on. The name of the tag is a unique field. If you have a tag that you use on one table, unfortunately you are unable to add the same tag to another table.
We have had a reasonable amount of feedback requesting the ability to add the same tag to multiple tables. I created a feature request ticket for this yesterday based on another post. I’ll “+1” you on the request as well.
-Audisho