Adobe Manages Services (AMS) and AEM as a Cloud Service (AEMaCS) are different offers by Adobe.
While AMS is more of a hosting offer for "classic" AEM 6.5 (similar to on-premise setups but run at/by Adobe), AEMaCS is a Software as a Service (SaaS) offer. Also AEMaCS has quite some differences compared to AEM 6.5 .
For additional details on AMS, please refer to this documentation  or ask your Adobe representative.
For additional details on AEMaCS, please refer to this documentation  (or ask your Adobe representative).
Creating and managing the AEM environments within these programs. Refer toManaging Environmentsfor more details.
Creating and managing the pipelines for deploying the customer code and the related configuration to a specific environment. Refer toConfiguring your CI-CD Pipelinefor more details.
Being notified of important lifecycle events for these components (for example, product updates).
Cloud Manager creates environments in datacenters across many geographic regions, providing for global coverage. CDN Points of Presence (PoPs) ensure low-latency content delivery for customers located all over the world.