The software is the same at its core.
But OnDemand/Cloud is a "managed service" - you sign up and that's it, you don't have to think about servers, infrastructure, backups, upgrades or maintenance. (On the point about upgrades, Atlassian release to Cloud when their code is ready, so it's usually ahead of the latest on-premise download). You still need admins, but the low-level "provide a Jira" stuff is done for you.
You are limited on Cloud though - there's a short list of addons you can add, and you cannot customise any code. You're restricted to running it within certain boundaries.
In 2014 it was true, that Agile Poker for JIRA wasn't available in JIRA Cloud but since May 2016 it's no longer the case. If you are still interested in this add-on take a look at it on Atlassian Marketplace and check out the 2min video below:
Mateusz - Agile Poker for JIRA developer
Remember that time you realized it was possible to refresh your Jira data in Google sheets with just one click? What if we told you that you can now get the latest data with no clicks at all?! Zero! ...
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