Oracle offers the following Exdata deployments for their customers
Exadata On-premise
Exadata Cloud@Customer
Exadata Cloud Servces ( OCI + Exadata Service)
Exadata on-premise
In the traditional On-Premise Exadata, Exadata Database Machine is in the client’s datacentre and is the client’s responsibility to manage the Exadata hardware with Oracle.
Customer who would like to avail cloud service and at the same time, they dont want to expose their data in the public. Exadata machine runs in customer datacentre with cloud feature enabled