For the New Implementation, there are two versions of the methodology guidance, one for cloud and one for on-premise.
These two new implementation methodologies succeed the previous guidance SAP offered in ASAP methodology for on-premise and in the SAP Launch methodology for cloud solutions. SAP now supports implementation projects with these different flavors of SAP Activate.
The on-premise version supports SAP S/4HANA and SAP Business Suite, and other on-premise solutions.
The Cloud Methodology supports the cloud editions of SAP S/4HANA, as well as SAP SuccessFactors, SAP Hybris Cloud for Customer, and Ariba solutions.
System conversion is designed only for an on-premise deployment model.
Landscape transformation is a scenario that supports both on-premise and cloud editions because the customers may decide to use certain capabilities in the cloud and certain capabilities in on-premise and integrate those solutions.