Normal backups copy the files and mark each file as having been backed up. Basically it leaves evidence behind of the backup process so that you don't waste time backing up files that don't need to be backed up.
A copy backup copies the files but does not mark them. So copy backups put the responsibility in your hands for knowing what has been backed up and when.
An online backup copies the files over the internet to offsite storage (so that any localized data loss will not affect your backup).
There is also the idea of a local "online backup", which has a completely different meaning. In this case it means that the backup remains connected to the system that is being backed up. For example, you could back up your server drive to a separate internal hard drive array. Then, in the case of a hard drive failure, you could restore the drive from your internal "online" backup extremely quickly.