The following (current/2018) REST API works great with the Microsoft hosted version of Sharepoint (https://yourcompany.sharepoint.com):
https://docs.microsoft.com/en-us/sharepoint/dev/sp-add-ins/get-to-know-the-sharepoint-rest-service
Does anyone know if this SPECIFIC API also works with/supports Sharepoint 2016, 2013, and/or 2010?
That set of operations should work with Sharepoint 2016. SharePoint 2013 and SharePoint 2010 have its own set of REST operations. Of course the methods have evolved but the apis are quite similar. For example SharePoint Online (and on-premises SharePoint 2016 and later) REST service supports combining multiple requests into a single call to the service by using the OData $batch query option, but on SharePoint 2013 on premises batch was not supported.
In this link you'll find the list of operations and samples for the SharePoint 2013 REST API:
SharePoint 2013 - REST API reference and samples.
Please watch the video in the link as it's a good introduction on how the API evolved. One thing to notice is for example how the old WCF "REST" api changed from
- http://contososerver/_vti_bin/client.svc/web
to this one
- http://contososerver/_api/web
Here are some links for the documentation about the SharePoint 2010 "REST" API:
So to finish answering your question, that specific link wont work for SharePoint 2013 and SharePoint 2010 (Some examples might work, but depends on the operation/method)
SharePoint 2013, 2016, 2019 and Online REST is almost all the same, although there are newer features in each version.
SharePoint 2010 had its own "flavor" of REST, with is still largely supported in the newer versions.
2013 and later requests look like "http://yourserver/sites/somesite/_api/..."
2010 REST looks like this: "http://yourserver/sites/somesite/_vti_bin/ListData.svc". (At least for lists.)
2007 and 2010 web services calls seemed to more for internal use between SharePoint Designer, Word, Outlook, etc and SharePoint. There was a real lack of consistency. 2013 and later are much more consistent and are for general developer use.
I have a "REST Tester" with lots of sample SharePoint REST calls SharePoint that I use regularly against SP2013 - 2019 with no differences in the core REST calls. https://github.com/microsmith/SharePointRESTtester
