In the TMMi framework, a Specific Goal is unique to a particular process area and represents the essential outcomes that must be achieved for that process area. In contrast, a Generic Goal applies across multiple process areas and ensures that the processes are institutionalised, managed, and aligned with broader organisational objectives. Generic Goals help maintain consistency and effectiveness of processes across the organisation, while Specific Goals focus on the particular needs of an individual process area.
Reference:
"Generic goals are called 'generic' because the same goal statement appears in all process areas. Specific goals describe unique characteristics of a process area".