Much like Web 2.0, cloud doesn't have a technical definition.
> There's an important difference, and people need to stop using them interchangeably.
People need to stop using "cloud" altogether.
Since as long as I remember and probably even before that, when explaining networking to executives, marketing and other technically challenged people, we use drawings. In these drawings the part representing the internet is for some reason drawn as a cloud, probably to convey that some magic we don't want to get into the deatils happens there.
Now you've got it, the cloud, a.k.a. the internet symbol for ignorant people.
(However if I own a couple/few of these boxes at different sites and they all sync up to store things redundantly then the line is blurred just a bit. The Synology devices are certainly capable of that.)
There are certain things I do host within my own ftp server, but I just use my web host which I have 10GB of disk space but am only using maybe 10 meg for my personal site. I wouldn't go to the extent of my own server unless it was a real business requirement, I'd be fine just putting on Dropbox/Google and if it was sensitive info then I would encrypt the files first - either 7zip or Truecrypt.
The sharing features were then enabled with a few clicks on the appliance's locally hosted (ExtJS) web application. This step was much less work than going around to every PC in the home and office installing Dropbox.
Usage-wise, I find it to be less work to share something via my Synology than with Dropbox, particularly because A) I don't need any special software to share something from any computer in the world, B) most of the time my files arrive instantly and C) there are no limits to the size of files that I can share. When I was still using Dropbox, I'd hit that limit often enough to make it a PITA to use.
That's why i just run my own "cloud" on my own premises. If I want to give someone access to a file, I just throw it on my Synology DiskStation and the receiver can get at it via FTP or HTTP client.