I don‘t think those books were particularly useful for understanding medical services at the battalion level, which is what I infer the terms "medic" to mean. Please correct me if I‘m wrong.
An infantry battalion or armoured regiment had its own Regimental Aid Post (RAP); in an infantry battalion, this included a Medical Officer (MO) who was probably a surgeon of some type, his batman, a Medical Sergeant, an orderly, a driver, and 20 stetcher bearers. Their job was to perform immediate first aid.
Casualties that could not be returned to the line would be sent back from the RAP to a Collecting Point where ambulances could safely pick up wounded, and then to a Field Dressing Station or Advanced Dressing Station for further treatment. Here, their weapons were collected, X-rays could be taken, etc. If a soldier could be returned to action quickly, he stayed here, if not, he went to a Casualty Collection Station (CCS) for further treatment and preparation for movement further back to a General Hospital, or possibly even a hospital in the United Kingdom.
Good info in the book THE BRITISH SOLDIER by Jean Bouchery, who has written a Canadian version THE CANADIAN SOLDIER advertised at
www.servicepub.com - it is still being translated into English and was supposed to be published last year, now they are saying by the summer or autumn.