Mental health is usually used to refer to "mental health" in life and "mental health" in medical sense. For example, he is mentally healthy. It means that he has a healthy sense of life and a strong will. His mental illness may mean that he is mentally ill.
Mental health is a psychological medical term, which also includes the above contents, but it is not commonly used in life. When people hear this word, they will have the feeling of "speaking like a book". But the message it conveys is no different from mental health. I'm afraid this phrase will appear more frequently in official documents. Example:
Advocated by the Mental Health Council of Canada (MHCC) and formulated by the Canadian Standards Association (CSA Group) and the Quebec Bureau of Standardization (BNQ), this standard is a set of voluntary guidelines, tools and resources to promote the mental health of employees and prevent psychological injuries caused by workplace factors.