In November 2016 Microsoft published two Updates for the old Sync Client OneDrive for Business (Groove.exe). You have to use this Sync client for local synchronizations from all SharePoint on-Premise variants. The same Sync client should be used to sync data from Office 365 Groups or Teamsites. According to the Schedule of Microsoft this should be changed till end of the year. There is a  Preview, to sync all data in Office 365 with the  Next Generation Sync Client: Team-Sites, Groups and also data, that is shared with me you may sync with this version. Again, Microsoft will announce the GA at the end of the year.

 

KB3118350 Office 2013 KB3118341 Office 2016

So there is no description provided by Microsoft, what has changed !

Both Updates are valid only for MSI Installations, not Click to run.

 

Before 11/1/2016	after 11/1/2016
Version 15.0.4859.1000	Version 15.0.4871.1000

Be aware that the update in Download Center applies to Microsoft Installer (.msi)-based edition of Office 2013. It doesn’t apply to the Office 2013 Click-to-Run editions such as Microsoft Office 365 Home

To determine whether your Office installation is Click-to-Run or MSI-based, follow these steps:

1. Open an Office 2013 application, such as Microsoft Word 2013.
2. On the File menu, select Account.
3. For Office 2013 Click-to-Run installations, an Update Options item is displayed. For MSI-based installations, the Update Options item isn’t displayed.

You will found the file groove.exe here:  X:\Program Files\Microsoft Office\Office15
So the version for Office 2013 of the file should be 15.0.4871.1000 or higher.
And the version for Office 2016 of the file should be 16.0.4447.1000 or higher.

 

Remarks:

Round the globe there are several questions about the Next Generation Sync Client: When will this sync client available to sync data with SharePoint onPremise?

So, according to “Cloud First, mobile first” you will have to wait till 2017, and no, I have no answer, which version of SharePoint will be supported.