Standard first aid courses have the unstated assumption that professional help is no more than an hour away. While this is generally true in cities and perhaps in campgrounds, it is not true in the wilderness. Darkness, bad weather and terrain can all conspire to make evacuation times anywhere from several hours to several days.
The minimum skill requirement for our members is Standard Level First Aid (St. John Ambulance, Red Cross, or equivalent) but for the above reasons most Foothills SAR members eventually take Wilderness or Advanced Wilderness First Aid. These generally include two subjects not found in other courses: scene management and long-term care.
Scene management is the skill of quickly determining how many casualties there are and what resources they need (triage). The scene manager then tries to allocate the available resources in the most effective manner possible. Scene management is scalable from single casualty to incidents involving hundreds of casualties spread over multiple sub-scenes.
Long-term care refers to the skills necessary to support and comfort a casualty when professional medical care is many hours or days away. It includes assisting with all normal bodily functions: eating, drinking, sleeping and elimination. Since you may need to bring the subject to a trailhead to meet professional help, it also includes transportation, such as making a stretcher from available materials. Fortunately for all concerned, we rarely need these skills.
FSAR recommends that everybody take a first aid course of some kind. Even the most minimal course will teach you the basic principles of what to do and what not to do in an emergency and as such will help you to deal with medical conditions you may encounter. And the persons most likely to need your help are not strangers, but family or friends (or even yourself!). The amount of training you pursue will depend on how much time, money and interest you have.