What is the difference between an IT Process management specialist and a service delivery manager?

Delivery Manager is more in to delivery the service / product to the customer within the budget, time , scope and as per the agreed quality. He will have to ensure the team morale, SLA management and escalations management.

Where as the Process Specialist will have to ensure setting up necessary processes to be followed with regards to the agreement with all the stakeholders of the project.

Delivery Manager is an operational functional job that does provide resources to projects for example:Delivery Manager can be given additional responsibilities like procurement, vendor management and account management. 

IT Process specialist will have a specialized skills related to a specific process such as incident management ,problem management etc. They act as a process experts.