Backup refers to a copy of a file, stored separately from the original source, which can be used to recover or used in place of the original in the event that the original is damaged or destroyed. Mostly, you will be copying from one physical drive to another, and you can as well copy to an online location.
On the other hand, you are syncing means to copy or delete files either manually or automatically, in a bid to ensure that two locations have the same files. As for backup, you will be having the same files at the source and the target locations until there are changes to the original or source files. This will make the target files not to look the same with the original file.
At this point, a new backup will need to be done in order to have the same files at both locations. With syncing, you won't need to copy again if the source files are altered. When you sync, it takes care of any difference in the two files at both locations, thereby making them be the same.