2 wire RTDs are the least accurate of the three types as there is no way of eliminating or calculating the lead wire resistance. This creates uncertainty in the reading therefore 2 wire RTDs are generally used with short lead wires where accuracy is not the main priority, they are mainly used in Pt1000 to reduce sensitivity and uncertainty (struggling to get a still reading as it is literally too accurate & the reading wont stay still) but this means it will not be providing a very precise reading compared to 3 or 4 wire.
3 wire RTDs are the most commonly used RTD sensors, Assuming all three lead wires are the same the third lead wire calculates the average lead wire resistance throughout the circuit and removes it from the sensor measurement. This makes 3-wire RTDs more accurate than the 2-wire alternative, but less accurate than 4-wire, however in circuits with long lead wires where there are long distances between the detector and the reading, significant savings can be made by using a 3-wire construction.
4-wire RTDs are used in applications where high accuracy is necessary. In a 4-wire RTD sensor the actual resistance in each of the lead wires can be measured and eliminated leaving the exact resistance of the detector. The 4-wire circuit works by using the first two lead wires to power the circuit whilst the 3rd and 4th wires read the resistance in each lead wire compensating for any differences in lead wire resistance.