Please note that the ISMS responsible is a role an organization can create, or incorporate into an existing role, to cover at least these activities:
ensure that the ISMS conforms to the requirements of ISO 27001
report on the performance of the ISMS to top management.
As for CISM (Certified Information Security Manager), it is a certification issued by ISACA which evidences that the certification holder has a certain set of knowledge and experience on information security management, which goes beyond the requirements related to ISO 27001.
This article will provide you a further explanation about roles for ISO 27001: