Indeed, for a long time it seemed like SAP didn't "get" cloud. Having to sign long contracts and speak to an account executive to get access to their cloud platform (rebranded every few months, now "Business Technology Platform", BTP) was the way they did things. Contrast with Google, Amazon, etc.
I've not yet used S/4HANA Cloud (only the on-premise version), but it looks to me like it's just a hosted version of standard S/4HANA but with various restrictions on what you can customise etc. No real elasticity, cloud scaling, etc. SAP ERP has been multi-tenant since at least R/3 in 1992 (I never used R/2) so "Cloud ERP" smells to me like "we host it for you and call it cloud".
There are two versions, the on-premise landscape and the cloud version. The on-premise version makes sense sometimes. You can even deploy SAP platform to cloud foundry.
