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There are notable differences between the cloud solution and the server addon. While the most important ones are listed below, bear in mind that that may be others as well. Jira Cloud is evolving as we speak, and we'll evolve with it.
Less Routines
Unfortunately, not all the routines available on the server version also exist on the cloud one.
The routines that you can use on cloud are label with ps_cloud. Please note that there may be differences in the way the routines are called or on the return type, between versions. You'll find all the information in the documentation page of every routine.
We are willing to add other routines to the cloud version, so if you need any, don't hesitate to ask us for it. 
Asynchronous Processing Model
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Many of the routines found in Jira Server do access internal APIs, allowing PowerScripts to do crazy things, or even jump between plugins, getting and updating data everywhere. On cloud, we are limited to the REST Api Jira provides, and as of now, we know many are still missing. We're trying to cover as much ground as possible in the shortest time, but please, do engage with us and tell us what you need, it will bump priorities in our backlog.
The routines that you can use on cloud are label with ps_cloud. Please note that there may be differences in the way the routines are called or on the return type, between versions. You'll find all the information in the documentation page of every routine.