Sort of - the process for both is "get the data out, set up a new system on the new server, then get it into the new server".
But https://confluence.atlassian.com/jira/migrating-jira-to-another-server-151126305.html is a better guide to the Server side because it talks about all the things that you need to think about (Cloud handles a lot of that for you, but relies on export/import. Server needs you to do more, but the data can be a lot easier to move)
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