What are the application difference of the circuit breakers which have difference "Circuit Breaker Characteristic Trip Curves"
The Application Differences are Resistive Loads, Transformer Loads and Motor Loads.

The inrush current for each of these loads is very different. The resistive load could in theory have very little in rush current at turn on. So the circuit breaker does not need much headroom .

The transformer can have an inrush 10 to 50 times the normal current. But it depends on the transformer and the load it's driving.

In fact most coil devices have an inrush current. So the curves allow you to pick the right circuit breaker that allows the load to start (a motor is a good example) with out having to specify some really high value circuit breaker based on the momentary in rush current, but rather choose it based on the normal load. (Needing a 100A or 500A circuit breaker for a 10A transformer is not good from a safety point of view)

Incandescent light bulbs also have an inrush current that tends to not be as bad as a transformer.



Edited to change "any coil device has" to "most coil devices have" See comments.