Now I know where you are coming from the explanation is easy and is focus oriented.
OKAY - DRABC as you surmised is for the scene of the accident. It is the bog standard mnemonic used to teach lay people about resuscitation. It does have a place here though because some burns may be caused by substances hazardous to ANYONE coming in contact with the agent or even with the fumes
A case in point may be the acid burn where the acid is still on the skin of the patient and the patient needs to be throughly washed down first. Usually this is done at the scene but you may not be so lucky. Hydrofluoric acid is one hazard that springs to mind
The last site also has some "ABC's in it.
ABCDE is the bog standard assessment criteria taught for all Emergency Nursing courses and is more specific to trauma cases. Sheehy will have ABCDE in other chapters I know I have Sheehy here at home it is a good book. You would use it in the case of a trauma + burn i.e. car fire following MVA Pt who while on fire ran and fell (not an uncommon scenario)
The last one is a very specific one for primary uncomplicated burns. In fact they have with the inclusion of infection and pain management included more of a secondary survey.
I would break my answer up into primary survey - DRABC (especially as you have no information on the mechanism of the burn) and leave the (Disability, Exposure, Pain management, Infection etc) as a secondary survey.
Hope this helps.