Have you ever used the Send To function in a document libray to send a copy of the document to another library? Maybe you have used explorer view to copy or move a document between libraries. If you have set up the same site columns in the destination site and library then you should see those metadata values set on the source document, brought across on the document copy. If some values are missing and you are scratching your head wondering why, then think back to when you first created those site columns. Did you change the name or one at some point? Even if you changed it back to what it was, or to match the site column name in another site, SharePoint still sees the column with its original title. You need to delete the column that was renamed and recreate it with the matching title. Make sure that the site columns also have the same metadata values on each site/library and then all metadata selections should come across with the copy/move.
I hope you caught it early enough to avoid some serious document metadata updates 😉 Goodluck