Today’s healthcare ecosystem is filled with references to and examples of telemedicine and telehealth – in some cases, the two terms are used interchangeably. Whether they mean the same thing is a topic of considerable debate.
I am not sure if the question refers to 'healthcare' and 'telemedicine' or 'telemedicine' and 'telehealth'.
Differences in terminology are basically a matter of the context in which it is used.
My take on this (not necessarily right) is that 'telehealth' is referred to the distant monitoring of the 'health' of individuals (irrespective of healthy or ill) and 'telemedicine' is related to the practice of medicine in remote areas (or not so remote) by remote means. Thus, 'telehealthcare' would be the assistance to health issues by remote means, and a synonym of 'teleassistance'.
Examples of these concepts would be: a) telehealth (i.e., monitoring exercise routines or diet through mobile apps or wearable devices.); b) telemedicine (i.e., a technician doing a retinography in a remote location which results would be interpreted by a specialist in another location, operate remotely by a robot interface, etc.); and c) telehealthcare (e.g., conducting a medical visit and examination through video conference on the internet.)
In my opinion, they are not interchangeable, although they try to convey different context that generally overlaps.
To add to Francisco's great reply, "Healthcare" is a very broad term of which "telehealth" is one of many subsets. The Oxford Dictionary defines Healthcare as "the organized provision of medical care to individuals ..."
I have also found that many authors disagree about the terms telehealth, telemedicine, eHealth, telemonitoring (the list goes on). I believe that the WHO definition still treats telehealth and telemedicine as synonyms, which is rather unhelpful.
The UK NHS has developed a new overarching framework called Technology Enabled Care Services (TECS). However, this framework concerns itself exclusively with the use of technology to help people manage and control illness (thus excluding all technology designed to prevent illness/disease).
The framework divides healthcare technology into five groups (defined on page 21); Telehealth, Telecare, Telemedicine/Teleconsultations, Telecoaching, and Self-care apps.
Although I have encountered minor problems in this framework - where the project I'm currently working on probably falls between Telecoaching and Self-care apps - this is one of the most succinct overviews I have encountered.
To add to the great answers above; telehealth is a more broader term that include all types of encounters in addition to exchanging health information. Telemedicine refers mainly to the processes of diagnosis or management of medical and clinical conditions, while telehealth refers to the broader perspective that include providing patients with tips, information and advice to keep their health better.
Some authors classify telemedicine as curative (therapeutic) and telehealth as protective (preventive). For example, telemedicine deals with existing conditions more, while telehealth deals with pre-conditions, such as life style, habits and healthy behaviors.
It is still true that many people use the two terms interchangeably, which is not a mistake, rather it is a common practice.