Ok! so whats in a name, if that's what its called that's what I'll get.
Trouble is over the years all the names have  meant different things to different people, add language misinterpretation and regional references plus the fact that many Paraffin Heater manufactorers called them Oil heaters, they can be excused, Oil fired central heating wasn't around then  
A Basic guide for UK users
Kerosene 
 
A generic word for any flammable liquid produced by the Oil industry, the word is also used in the US and Europe to mean Paraffin, Asking for Kerosene in the UK usually gets you Heating Oil ( not suitable for Paraffin Heaters and Lamps)

Paraffin 
Refined to comply with British Standards it is usually supplied in 4 or 5 Litre Plastic containers and has 2 Grades.
Standard normally straw coloured suitable for all Lamps and Heaters.
Reduced Odour normally has a Blue tint because a lot of the Sulphur has been removed. Burns at a slightly higher temperature with less of the characteristic smell.

Lamp Oil
This is where the confusion starts again, it's not Oil it's refined Paraffin, normally sold in 1 Litre Black  Bottles,  Crystal clear, no odour and very little taste, a better Name would be Paraffin Lamp Fuel, but it doesn't look as nice in the advertising.
Use only the clear version in Paraffin Lamps
Coloured and Perfumed Lamp Oils should only be used in Oil Lamps# as Directed, NEVER in a Paraffin Lamp
#  see Oil Vs paraffin Lamps The difference