Suppose I want to backup the Documents folder on my old computer, partly for backup, and partly so I can reference items in on my new computer. What's the difference between using Backup vs Sync for this folder? Thank you!
At the beginning Dropbox is a sync service, so "Backup" is... backup in quotes 😃. Dropbox application keeps in sync everything within Dropbox folder and nothing outside. That's why if you want to sync something, it should get moved into Dropbox folder. So called "Backup" helps you with automation of this process. There are some additional system settings, get set behind you, because special folders are on focus and folders are moved. That's all, nothing else.
I would advise you, if you want to sync something, better sync it "by hand", so unexpected results are less likely. 😉