Oracle backup with RMAN Options?
A Cold Backup is making a copy of the files with the database closed. These commands are both for hot backups using RMAN.  They are both preferred over cold backups due to their flexibility.  

The difference between the two commands is whether or not archive logs are backed up.  If you need be able to recover to any point between your backups or anytime after your most recent backup, then you will need to be in archivelog mode.  If you are in archivelog mode then something needs to be done to backup those archive logs and use should use the PLUS ARCHIVELOG syntax.

It is advisable to periodically test a recovery as well to make sure your backups are working and you can recover.