Architecture of SharePoint Online
SharePoint can be deployed in different topologies:
- SharePoint Online
- Hybrid
- Azure/IaaS
- On-premises
The following image shows how responsibilities are split between Microsoft and the customer depending on the selected topology:

SharePoint Online
SharePoint Online is a software as a service (SaaS) product that comes with your Office 365 tenant. The following image depicts a typical scenario in most organizations that uses SharePoint Online, with synchronized users to Azure AD and the source of the identity being the on-premises AD:

SharePoint in Azure or an on-premises hybrid
A SharePoint hybrid is a way to integrate your SharePoint Server 2016 on-premises farm with your SharePoint Online tenant by sharing some of the components of the two". You can deploy your on-premises farm either in your data center or on Azure as an infrastructure as a service (IaaS).
SharePoint hybrid
The following image represents an organization that has SharePoint on-premises and is connected...