I am being migrated from SharePoint Online Dedicated to Microsoft's Government Community Cloud (GCC). It seems like the Dedicated environment used a Nintex farm solution, but the GCC will be using a SharePoint add-in. Is that correct? Are both of Nintex's applications the same in terms of functionality? I use about 30 different Nintex workflow activities and I would like to find out if they are all in the GCC solution. If not, I would like to try to understand how much of my workflows need to be re-written.
The dedicated infrastructure was indeed customer-specific, dedicated infrastructure (https://technet.microsoft.com/en-us/library/dn151711.aspx), while GCC are hosted as the "multi-tenancy", so customer has no access o the server-side. So you are mostly right, about the fact, that first you had on-premise Nintex and now your moving to the Nintex for O365.
And unfortunately no: the Nintex "Online" version (the add-in) and farm solutions are having many differences. In general you can reproduce all functionalities, sometimes using workarounds, but in details there are many differences. Please, take a look at my latest blog post: https://community.nintex.com/community/build-your-own/nintex-for-office-365/blog/2017/04/14/nintex-m..., hope it will put more light on your question.
I left that employer, but my understanding is that they build an on-premise SharePoint farm and migrated Nintex Workflows from SharePoint Online GCC to on-premise. I believe a contributing factor was also the cost of using Nintex in SharePoint Online.