There is no difference by tier, no. I'm not sure it is actually called out specifically on any particular page, but it is mentioned in many. I do know my 10 user play version is identical to my unlimited clients version.
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The on-premise application itself does not change based on the number of users, just your licensing needs. If you need to move from Jira Server to Jira Data Center (which, unless you have more advanced needs you haven't mentioned, isn't necessary to accommodate your number of users) you'll need to reconsider your deployment; otherwise, you'll just need the most up to date version of Jira Server:
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