What fire extinguisher to use when a person is on fire?

Yes. But there are different kinds of fire extinguishers. If the person's clothing is on fire, you would use a water-type (Class A extinguisher). If they were covered in flammable liquid or gas (e.g., propane), you may need to use CO2. Do not spray CO2 near a person's face, to avoid them inhaling it and damaging their lungs.

If you use CO2 on them for a prolonged period of time they may suffocate due to the lack of oxygen or if you are too close to them you may freeze their skin. Commonly known as CO2 burn, because it will feel like the skin is on fire when it is actually just the capillaries freezing, like frostbite.