Re: Alfresco CMS provide both on-premises solution and cloud solution, is this correct?
"We want to use both for our website." - That is a pretty vague way of describing your use case and does not allow anyone to make a qualified judgement. Alfresco is first and foremost an ECM platform with a heavy focus on collaborative DMS and related functionality. It is not a WCM system to build web sites on.
Alfresco provides a cloud-based service for Enterprise customers, and you can of course install Alfresco on your own system (which may or may not be cloud-hosted).