A backup copies files in one direction: from the source to the destination. It does not delete files in the destination. It will replace files in the destination with newer files from the source and also add files to the destination that are missing.
A mirror also copies files in one direction: from the source to the destination. It does delete files that are only in the destination. Like a backup, it will replace files in the destination with newer files from the source and also add files to the destination that are missing.
So a mirror is the same as a backup, except for the case where you have files only in the destination, i.e. you only have backups. Those are deleted. For example, you are copying files from your computer (source) to the cloud (destination). You delete a file from your computer (the source), e.g. a document. That same file is already on the cloud (your destination), e.g. you've already run a backup or mirror before you deleted it so a copy of the file was made. If you have a backup profile, then when you run it again it will not delete the file from the cloud. However, if you have a mirror profile, then it will delete the file from the cloud.
A synchronization copies files in both directions: from the source to the destination, and from the destination to the source.
Intelligent Synchronization copies files in both directions, but it also keeps a history of where files were during the last synchronization. This allows for much finer control over what actions to take based on what has changed, and also allows it to detect changes such as the file only being modified in the source or destination.
It is advisable to use Intelligent Sync instead of the "old style" synchronization but note that SyncBackFree does not support Intelligent Synchronization.