Confused now. I was always under the impression that HEMS was the generic term for the Air Ambulance services (charities)
Certainly in this part of the world the same airframe (G-HEMS at the moment) does both roles i.e. attends emergencies and is used for hospital transfers!
We have been done this route some time ago but essentially its like this (And this is my opinion and my definition as I can't remember what ATP 10D says but Thats the authoritive document)
A Rescue is a transfer of a person or persons from a hostile environment to a safe environment.
A CASEVAC is the transfer of an injured person from a safe environment to a medical facility.
A MEDEVAC is the transfer of an injured person from one medical facility to another medical facility.
Does it matter ? Yes indeed because in the UK it all depends on who pays for it.
Gannet SAR flight is the busiest SAR flight in the country. However, most of their jobs are CASEVACs or MEDEVACs. Now, that doesn't demean the fact that they are busy in any shape or form, thats just the way it is. But, does this contract (when it is written) allow for the new SAR aircraft to conduct CASEVAC and MEDEVAC ? i.e. if a lady is pregnant and she lives on the isle of Arran - is the new SAR cab going to scramble from Glasgow (in $hitty Weather - and fly under the Bridge) to go and transfer her to a hospital. At the moment the answer is yes. What will be the answer in 3 years time?