It is always related to Microsoft Groove, introduced with Office 2007, or its successor products: it was renamed as SkyDrive Pro, and became SharePoint Workspace after a 2013 lawsuit by the UK's BSkyB for trademark infringement. It is not part of Microsoft's Groove Music app for Windows 8, 8.1, or 10, (which uses 'ZuneMusic' in its module names). If you have 'groove.exe' on your system, what you have differs, depending upon your version of Microsoft Office, how it was installed, and what kind of workspaces or libraries are being synchronized.
The genuine groove.exe file is a software component of Microsoft OneDrive for Business by Microsoft Corporation.
