You click on a SharePoint document library (SharePoint Online and SharePoint Server 2013) on the "Synchronize"-Button and on you client device opens SharePoint Workspace 2010?

This could happen. But the following requirements must be met:

• you have installed Office 2010 on your device.
• you have also installed the standalone program OneDrive for Business.

and

• there was an update for Office 2010 installed.

This update entered incorrect values on some keys in the registry.

Remedy:

You start  immediately after the update of Office 2010 a manual repair of OneDrive for Business.

Background:

The first program, which synchronized files between computers, called Groove. Here you can find countless information on the program (most in German language). After Microsoft bought Groove Networks (including his CEO (Ray Ozzie), who had later taken over from Bill Gates at Microsoft), the product was  called SharePoint Workspace 2010, and files could still be exchanged between computers, but for the first time there was a client program, which may synchronize data from the SharePoint Server (2010) making these files available offline. Next step was SkyDrive Pro (and lost a lot of functionality) and from SkyDrive Pro the last step was OneDrive for Business. And today you still can find Groove.exe on your system.

SharePoint Workspace 2010	<–>	SharePoint Server 2010
OneDrive for Business	<–>	SharePoint Server 2013  / SharePoint Online

You could buy SharePoint Workspace 2010 separately, but it was also part of Office 2010 Professional Plus

As Microsoft continues to mend vulnerabilities for Office 2010 and this is distributed on a monthly basis, incorrect values ​were written ​in the registry when updating and this must be corrected. To repair OneDrive for Business, see Panel- Programs – Programs and Features … right mouse button, then "Change"

Select quick repair and then Click Repair.

Then you may click as usual, on each new SharePoint document library in the web browser for synchronization.

One Microsoft?

Unfortunately, not yet. Otherwise the Microsoft managers of OneDrive for Business would say to those responsible for Office that under the above circumstances, these registry keys do not need to be set. On reason  could be, because the Office people work in Redmond, but pursue OneDrive for Business developers work on the original location of Groove Networks in Cambridge MA near Boston.