The main part of diesel fuel is kerosene, which produces thick black smoke, and gives that smell that is commonly associated with diesel. most likely if it is white smoke, it is antifreeze, if it has a blue tint to it, it is oil. the smell of burnt diesel is rather strong so it could cancel the burnt oil smell, or on the other hand it could be coolant, because burned coolant doesn't have a strong smell. I would check your coolant and oil levels, and check your coolant for having oil in it.
My diesel engine is not smoking. If your's is smoking there can be a variety of reasons, you would need to be more specific in your question
The engine is burning oil
the smoking is most likely caused by the engine burning oil.
You can convert a petrol engine into a diesel engine by changing the fuel injectors. The fuel filters will also need to be changed.
changed engine
if the engine is smoking and overheating the head gasket is blown or you popped a freeze plug
Blue smoke is burning oil.
Petrol or gasoline in a diesel will cause internal engine damage. if petrol is used in diesel engine it may cause explosive sound with burning ....bcz high compression ratio ......
make the fuel sufficient burning
You are burning coolant. What vehicle? did you do a compression test?
Diesel smoke is often caused by fouled injectors, in which case the smoking can be cured by pouring a dose of good injector cleaner into the fuel tank on the next fill-up, and change the fuel filter, too. And change the engine oil and filter!
If the engine is diesel, no that is normal. If the engine is gasoline, yes it is probably burning oil.