In ITIL V3, a service strategy is specific to services themselves e.g., what service will be delivered to meet customer needs. It is part of the overall IT strategy. In comparison, the ITSM Strategy defines how the services are managed. Remember there is an organizational strategy that defines the purpose and direction of the organization and from that, plans (really, these other strategies – IT Strategy, IT Service Strategy, ITSM Strategy) will be defined to meet those goals.
The Service Strategy designs the services to meet organizational and customer goals and then executes those services and ensures they continue to meet the customer and organizational needs.
The ITSM strategy ensures the processes that are necessary to support and manage those services are defined, implemented, managed and improved, if needed.
Therefore, it is the atmosphere of the organization, defined in the organizational strategy (mission, vision, goals, objectives), that drive what functionality is in place (IT Strategy), what services are delivered (IT Service Strategy), and how service are managed (IT Service Management Strategy).