http://www.etrailer.com/tv-faq-2-wire-vs-3-wire-system.aspx

A 2 wire system has one circuit a 3 wire system has 2 circuits....

Not really - the 2 wire system I assume he is referring to runs off the 4-20ma "loop power", and the 3 wire system needs power beyond what the "loop" can supply. The third wire is +24VDC. If you wish to consider that positive power lead as a second circuit, you may. But, I feel it is all part of the same circuit.

Occasionally you get burned on the 2 wire systems. Had a control valve with so much impedance, on a recent project, it drug the AO card loop voltage down so low the unit would not function. This really should have been a 3 wire system. Major instrument/valve manufacturer got me on this. Neither their literature nor the AO card manufacturer had a warning on this.

The difference is one wire. (Can I get a rim shot?)

This sounds like homework problem. Since you don't provide enough information to tell if this is homework or which of the myriad of ways that a circuit could use three or two wires, I'll explain one arcane method that you're probably not interested in. This way if this is a homework assignment and you copy this, you will likely get it wrong because the question was about a different problem.

Often one will want to measure a small voltage or resistance difference produced by a sensor that must go through multiple disconnects between sensor and electronics. If the sensor could be placed near the electronics then just two wires could be used because the added resistance of the wires and voltage produced by dissimilar metal contacts will be a minimal effect compared to the sensor signal. When sensor and electronics must be very far away (100's of meters is not unusual) then three wire sensing can be used with the extra wire used to measure the added effect of the wire length voltage drop. This measured effect is then doubled (to simulate the non-monitored cable) and subtracted from the value read. Now wire changes can be cancelled out to some modest level.