A Safety Management System (SMS)  aims to reduce and manage risk in the workplace. In a way, it can be considered part of an HSE management system; however, an HSE management system also considers health.
There is also a difference in where they are used. While both terms are used worldwide depending on preference and legal provisions, the term “safety management system” is more used in the US, while “HSE management system” is more commonly used in the UK, but sometimes used in the US with  Occupational Safety and Health Administration (OSHA) regulations.