Transferring innodb table
You cannot rsync a running database, but you know that since you said you stopped it.

I'd you rsync with the mysqld not running (or from a snapshot), you have to rsync the ib_logfile* and ibdata* files from the datadir. Then there is no need to DISCARD/IMPORT TABLESPACE either.

For a copy without shutting down the database, xtrabackup is probably the most efficient solution.

If you have existing databases on the target, you will need to mysqldump --no-data dbname and import on the target in order to re-create the table structure metadata, but you will have FLUSH TABLE ... FOR EXPORT in the source before copying across. Then they will be clean and can be imported with ALTER TABLE ... IMPORT TABLESPACE