Every soldier has a first aid kit which is used to prevent someone from bleeding out for example. It just contains some bandages and other things to dress someone's wound, so the wound doesn't get infected. While the medkit, used from a medic, contains much much more things.
That's also the case in ArmAIII. If you use a first aid kit, it won't heal you, it just stops the bleeding and prevents you from bleeding out but your health stays the same. A medkit stops the bleeding and heals you back to 100% health.
Also with ArmAIII's new inventory system it makes sense that they've given these two special classes a seperate toolkit. Because they both weight something and need to be carried in a backpack which reduces their fatigue. Else you could magically heal someone when you've got nothing but your underwear.