I would suggest that the smell of the smoke would be highly indicative. Diesel fumes, hot fuel, coolant, oil vapour, hot electrics, scorched insulation, burned PCB, charred wood etc all have a different smell and can be highly indicative, if you know what they smell like.
In terms of probability oil spilled when filling the engine is the most likely cause. Exhaust damage is possible. Checking rubber hoses for witness marks caused by rubbing on things would help - if there's no mark than the hose is probably ok and not leaking. Checking hose couplings for leaks is also worth doing.
Also if you've got access to an IR thermometer then this can help, if you know how to use it and know what the readings are telling you.
Others may have a different opinion.