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Yes and no. This is quite a complicated answer because you need to understand a bit about the underlying architecture and what an app really is.
It's easier to start with server, as a cmparison point. Server applications are written in Java, so yes, you would write your app in Java (or related languages like Groovy or Scala if you implement a bit of support for them). Your app is then uploaded on to the server, and loaded and run by Jira (or Confluence, Bitbucket, Crowd, etc)
Cloud has a different plugin framework. We can't write Server apps and install them on Cloud. Only Atlassian can install that type of app, and they mostly don't.
A Cloud app installation is actually not a lot more than a descriptor for a (very limited) set of changes, or, more frequently, a link back to a service running on someone else's systems..
So, technically, you can write apps that can be "installed" on Cloud in any language you want. But they'll be running on your hardware, and talking to Cloud over its REST interface, not actually running on Atlassian's servers.
Your best option for writing for Cloud is to completely ignore what server does and start again. The current framework Atlassian has is "Forge", so I wouldn't bother with the older options, just get stuck in at https://developer.atlassian.com/platform/forge/
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