Think about it for a minute, if you are out in the wilderness it is unlikely that in the event of a medical emergency that you are going to be able to get in touch with paramedics any time soon. Wilderness First Aid training courses are generally more intense for that reason. They also equip you with the tools that would be necessary to get yourself out of the situation that you are in.
The Wilderness First Aid training courses cover such things as Anaphylaxis which is a severe allergy, broken bones, bug bites, heat exhaustion, heat stroke, hypothermia, frostbite, tick removal, and snake bites. Courses such as these teach much more detail about health emergencies that might arise in the wilderness than a standard First Aid training course would offer. It deals relatively with nothing more than issues that would be of concern to those who frequent the wilderness.
It is quite frequently the case that those who are in the wilderness may not be able to access outside help for days and of course there is a greater risk involved in these types of locations than there is in a typical daily living situation. These people put themselves at greater risk.
There are three organizations that provide intense First Aid training courses designed specifically for those in the wilderness; they are much more stringent programs, Wilderness Medical Associates, Wilderness Medical Institute, and Wilderness Medicine Outfitters. First Aid training courses will vary depending on exactly which remote location that you plan to be in. They will also teach you how to prepare your own first aid survival kit which will vary depending where you will be.
Anytime that people are traveling in the wilderness they should always travel in at least pairs or more with at least one person trained in wilderness first aid and should also have a first aid kit specifically designed for the location that they are in. It probably would not hurt to do some research on the location as well and see what types of hazards are in and about it. Are there poisonous snakes, poisonous plants, dangerous animals, etc. This way you can be prepared for any medical emergency.
Rather than a standard first aid kit you might want to consider what is called a trauma bag. It is understandable that you want to travel light but this type of bag has much more items inside of it that could greatly increase your chances of survival.
A first aid kit with a few band aids, gauze, and some sterile alcohol wipes is likely not going to save your life. Pack it as light as you can but make sure that it does have the basics but also some pain medication, fever reducers, quikclot, activated charcoal, syrup of ipecac, and an Epepin.