Hi @Aron,
a cloud database has functionality at the IaaS level and PaaS level. The options you have and how you interact with them are going to be different depending on the service model. It belongs to both. How you interact with a cloud database will be different depending on whether you are using an infrastructure (IaaS) or development platform (PaaS) environment. From a pricing and provisioning perspective, I think this is considered IaaS, but from a management perspective, it is likely more PaaS or even SaaS.
Check the below image to understand the cloud models:
