As terms, "eHealth" and "mHealth" focus on the tool (electronic, mobile, etc.) rather than the issue (health). I guess some years ago, you might have had tHealth (typewriter health) or pHealth (for pen, or pencil, or paper, as used in health contexts) :-)
Of course there are good reasons for focusing on the electronic or mobile aspects of the delivery mechanisms.
And there is a paticular value in distinguishing the tools used to deliver health when one considers the negative aspects - misuses of Big Data, artificial intelligence, automated translation, invasions of privacy and other ethical lapses enabled by the digital environment.
HIFA profile: Chris Zielinski: As a Visiting Fellow in the Centre for Global Health, Chris leads the Partnerships in Health Information (Phi) programme at the University of Winchester. Formerly an NGO, Phi supports knowledge development and brokers healthcare information exchanges of all kinds. Chris has held senior positions in publishing and knowledge management with WHO in Brazzaville, Geneva, Cairo and New Delhi, with FAO in Rome, ILO in Geneva, and UNIDO in Vienna. Chris also spent three years in London as Chief Executive of the Authors Licensing and Collecting Society. He was the founder of the ExtraMED project (Third World biomedical journals on CD-ROM), and managed the Gates Foundation-supported Health Information Resource Centres project. He served on WHO’s Ethical Review Committee, and was an originator of the African Health Observatory. Chris has been a director of the World Association of Medical Editors, UK Copyright Licensing Agency, Educational Recording Agency, and International Association of Audiovisual Writers and Directors. He has served on the boards of several NGOs and ethics groupings (information and computer ethics and bioethics). UK-based, he is also building houses in Zambia. chris AT chriszielinski.com
His publications are at www.ResearchGate.net and https://winchester.academia.edu/ChrisZielinski/ and his blogs are http://ziggytheblue.wordrpress.com and https://www.tumblr.com/blog/ziggytheblue