SMM or Social Media Marketing is a part (a subsection) of Digital marketing.
An SMM manager is only limited to social media platforms like Facebook, Twitter, Instagram, etc.
The SMM manager cannot do anything that is related to Social Media sites.
On the other hand, a Digital Marketing Manager focuses on all the aspects of digital marketing like SEM – Search Engine Marketing, SEM – Search Engine Optimization, eMail Marketing, Podcast Marketing, etc.
Both the Digital Marketing Manager and the Social Media Marketing Manager must be good at writing high conversion copy.
In conclusion, if it was in the Medical field the Digital Marketing Manager is more like a General Doctor who deals with all patients. On the other hand, a Social Media Marketing manager is like a specialist doctor for surgeries or radiology issues.