I found this KB https://support.microsoft.com/kb/2903984 which doesn't mention the term 'file' anywhere (except to refer to the downloaded installer file). It uses the terms 'library' and 'content':

The stand-alone OneDrive for Business (formerly SkyDrive Pro) sync client lets users of Microsoft SharePoint 2013 and Microsoft SharePoint Online in Office 365 sync their personal OneDrive for Business (formerly SkyDrive Pro) document library or any SharePoint 2013 or Office 365 team site library to their local computer. This sync relationship provides access to important content both online and offline. The OneDrive for Business (formerly SkyDrive Pro) client can be installed side-by-side with previous versions of Office (such as Microsoft Office 2010 and Microsoft 2007 Office).

I tried the installer. The installation process is branded all over as being a feature of Office.

Is there something other than the substring 'Drive' that gives the expectation of a fully generic file synchronization tool?