Sync vs backup

Hi all..

Can someone explain what is the exact meaning of sync vs backup ? I'm tying to get my head around this with Dropbox, (using Apple's iCloud to compare) as well to Carbonate, Backblaze etc.... To me, their the same.

For example, Dropbox only give you 2 Gig Free... Apple gives you 5Gig (excluding content in the iTunes & App Store)

However, when you sync documents, it appears on other devices (without making a copy on server)...

However, if you "Backup your IOS" device to iCloud you can "Restore it" later on a fresh IOS device (which means this backup *is* a backup)

Even though Apple doesn't advertise iCloud as backup service, it *is* one when it comes to backing up your settings, to later restore to a blank IOS device. But only in this case.....

Similarly, you access Dropbox on another computer/tablet, from any web browser, even though the original device is not on.

To me, this is a backup, because you can download to your computer even when its just the OS installed to get back everything. (based on the storage they provide)

is this correct ?.