All cables i.e. PVC, low smoke and FP cables, have conductors and insulation to manage the electrical current and voltage. Some also have extra physical protection, like steel wire armour. How is the difference determined?

The difference between low smoke and fire resistant cables is determined only by the application and performance required by the system itself. This makes for three groups.
FP is for essential services such as fire alarms, emergency lighting, life safety and fire fighting applications. They require fire resistant cables (e.g. Prysmian’s FP). These systems have to operate during a fire to detect the fire, alert people and help them evacuate and also help emergency services do their job. These circuits need to function fully and retain circuit integrity in the event of fire.
LSOH and PVC cables are for non-essential services that do not need to operate in a fire. These include all the usual power circuits in buildings for services such as general lighting or kitchen and office appliances like cookers or photocopiers.
These circuits are not essential for the safety of the public; they can fail in a fire with no increase in danger so they do not need to be fire resistant. For public buildings however, all cables need to be low smoke and zero halogen type but in domestic premises and for buried cables they do not, so PVC is acceptable.