Most of us are aware if SaaS, IaaS, and PasS but here is another term, DBasS.
Hosting, managing, and consuming a database in a cloud such as Oracle cloud platform or Microsoft Azure cloud, or Google cloud makes a database as a service.
DBaaS is database as a service. Hosted in a cloud, DBaaS takes full advantage of cloud computing platform such as flexibility, scalability, maintainability, and pay-as-you-go.
Most of the major cloud computing platforms including Microsoft Azure, Oracle cloud, Google cloud, and Rackspace provide database in a cloud.
Tesora is another great example of DBaaS. Tesora Database as a Service (DBaaS) platform is an enterprise-hardened version of OpenStack Trove, the native database service for OpenStack. This highly scalable, open and secure database as a service software offers you support for the databases your users are looking for along with the agility they demand today.
References
http://whatis.techtarget.com/definition/Database-as-a-Service-DBaaS