Inrush current occurs when a system powers on and experiences a spike in current. Motors, motor drives, amplifiers, power supplies typically have low impedance and the tendency to draw far more than their normal operating current. Capacitors in some of these systems can even effectively be a short until they are charged! The current spike can easily be 1 to 100 times the operating current of the device, so limiting that inrush current is crucial to device reliability.
Negative Temperature Coefficient (NTC) thermistors are often used to limit inrush current. They limit current with an initial high resistance, then as the thermistor temperature rises, its resistance lowers. That decrease in resistance is the negative coefficient part. NTC thermistors are desirable for the protection that is added with a low cost and simple solution. NTC thermistors can do the job in many situations, but they can fail to protect the system if power is cut and then returns before the NTC thermistor can cool. In that case the NTC would let too much inrush current flow to protect the system.
Positive Temperature Coefficient (PTC) thermistors may be better in some situations. If the reset time needs to be short, the PTC thermistor would be ready to control the inrush current where the NTC thermistor would still be hot and allow the inrush current. A PTC would be better in applications where the ambient temperature is greater than 65°C or less than 0°C. In those scenarios an NTC thermistor would be hot already and not have enough resistance, or it could be too cold and have too much resistance for the circuit to function. PTC thermistors generally cost more and require additional circuitry to function in their inrush current protection role.
In conclusion, inrush current limiting is an important part of protecting your equipment. NTC and PTC thermistors are two common ways to provide that protection. They literally work in opposite ways from one another, but both use the property of varying resistance due to temperature change. NTC thermistor designs tend to be simpler and cheaper, while PTC thermistor designs fit other applications and offer a higher protection potential, but at a higher cost. Your equipment, budget, and safety will be greater with inrush current protection from either NTC or PTC thermistors.