In IaaS service model. CSP is responsible only for the physical infrastructure.

Containers are code execution environments that run within an operating system(for now), sharing and leveraging resources of that operating system. While a VM is a full abstraction of an operating system, a container is a constrained place to run segregated processes while still utilizing the kernel and other capabilities of the base 0S. Multiple containers can run on the same virtual machine or be implemented without the use of VMs at all and run directly on hardware.
Reference: CSA Security Guidelines V.4(reproduced here for the educational purpose)

ISO/IEC 27018:2014 establishes commonly accepted control objectives, controls and guidelines for implementing measures to protect Personally Identifiable Information (PII) in accordance with the privacy principles in ISO/IEC 29100 for the public cloud computing environment.

Explanation/Reference:

This is a tricky question.
When using a Database as a Service, the provider manages fundamental security, patching, and core configuration, while the cloud user is responsible for everything else, including which security features of the database to use, managing accounts, or even authentication methods.
Ref: CSA Security Guidelines v4.0