They may be slightly different, but not by much. Since Confluence Cloud is always "up-to-date", you can always be sure that it is running the latest version of the Confluence API.
For Server, it might be slightly different depending on the version of Confluence you have installed (although it should be mostly the same especially for recent versions like 6.0). You can go here and choose your version of Confluence to see the REST API documentation for a specific version:
Hi team, I’m Avinoam, a product manager on Confluence Cloud, and today I’m really excited to let the Community know that all customers can now try out the new editing experience and see some of the ...
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