Will renaming a MySQL table to another database result in a full table copy operation on disk?

I understand that renaming a table within the same database will not generally result in a table copy... It's not clear to me if this holds true for renaming across databases. For reference, I want to move/rename a ~1TB table to a different database, and I don't want to initiate a huge copy operation. Will renaming a MySQL table to another database result in a full table copy operation on disk? Please provide an explanation or references if possible.