Alfresco Content Services (ACS) Community has Activiti 5.x as an embedded process engine. When Activiti (Community) and ACS are installed separately, there is by default no integration, apart maybe from the option of doing ReST calls from Activiti to ACS via a standard behaviour. Note that there has been a general communication (since ACS 6.0) that at some point, Alfresco is likely to remove the embedded Activiti engine in Community and replace it with a "limited / simple workflow capability". The company has for a long time followed the strategy of focussing on their Alfresco Process Services (APS) product (Enterprise only) for standalone, non-trivial process capabilities, which can integrate with ACS. Most recently, Alfresco has introduced / announced Alfresco Process Automation as a PaaS solution, which could be the successor to APS (no word on the long promised and often delayed APS 2.x yet).
Both Activiti and ACS can be installed on any Linux / Windows environment, whether desktop or server. For ACS, Alfresco has standardised on Docker-based images for deployments since ACS 6.0, and I believe all the Activiti Cloud (2 major versions ahead of the ACS-embedded Activiti engine) is also heavily dockerised.
To backup what @afaust has written: If you wish to trial the enterprise offerings, you can go here. You will also find links to download the community versions there too. The installation options for ACS are outlined in the docs. ACS also has additional Governance Services capability for both enterprise and community.
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