How to set up External Sharing same as Office 365 in SharePoint On Premise 2016?
The 'sharing' options have not changed between 2013 and 2016.
You could use standard Active Directory accounts and hand those out to non-employees. This requires a Windows User CAL or External Connector (last I looked, that evens out at ~60 users). On the SharePoint side, no licensing is required.
You could also federate using Azure ACS and develop custom code to handle sharing with accounts such as Microsoft, Facebook, etc. This is a fairly high development investment, though.
MSDN Forum Link Sharepoint Server 2016 - On Premise External Sharing