"Telemental health is a part of telemedicine.  So we can think of it as sort of a subspecialty of telemedicine.  And the definition of telemedicine, interestingly, is incredibly variable.

There was a recent literature review done by Sood et al. that identified 104 peer-reviewed definitions.  The authors concluded after reviewing these definitions that they could come up with a summary definition which is as follows:

Telemedicine uses communication networks for delivery of health care services and medical education from one geographical location to another.  It is deployed to overcome issues like uneven distribution and shortage of infrastructural and human resources."