This distinction is really without a difference. Dropbox consistently advertises themselves as both a syncing service as well as a backup service. Their tag line is even "Dropbox - Secure backup, sync and sharing made easy," with secure backup being ahead of sync and sharing. [1]
"Even if your computer has a meltdown, your stuff is always safe in Dropbox and can be restored in a snap.
In fact, if you're using the Dropbox desktop application, your files are backed up several times. The primary copy on your computer's hard drive is synced online and that copy is then backed up again for safety (emphasis mine). If you are using Dropbox to sync files between multiple computers, your files are backed up on those computers as well. If that isn't enough, Dropbox also keeps backups of all of your deleted and changed files too.
...
It's hard to imagine a scenario where Dropbox could lose your files. Hypothetically, let's say a nuclear bomb blows up the data centers where your files are saved. Even then, your files are still safe and sound on your computer and any other computers linked to your Dropbox account."
Clearly, though, Dropbox appears to have lost files (at least if we take it on faith that "these are bugs in Dropbox's syncing logic"), despite the fact that I see no mushroom cloud nearby.
[1] https://www.dropbox.com/help/122/en