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For non-user-facing aspects, there may be some differences between the platform. For example, in Jira Cloud, the number of search threads is hardcoded though it is configurable in Jira Server and Jira Data Center. All of the differences are documented in the User Documentation. In particular the Loading Your Jira Data page.

Do I need a new license?

You will need a new license if you’re moving to Jira Cloud since the Atlassian Marketplace treats the licenses differently. For more details, please visit https://www.atlassian.com/licensing/marketplace#general-faqs.