Well this topic certaintly has gotten mangled with contradictory info. It's more of an instrumentation topic than a PLC one. Let me take a shot at clearing it up...
Analog signal transmitters (pressure, temperature, flow, level, etc.) come in two basic types: 2-wire and 4-wire.
The significant difference is that a 4-wire transmitter is powered. That is, it has terminals for power connection on the transmitter. It can be 120vac or 24vdc. The signal from a 4-wire transmitter is powered from the transmitter. No loop power supply is required.
On the other hand, a 2-wire transmitter does not have a separate power connection. It usually only has two terminals (+ & -). It derives any power it needs from the loop power. Therefore a loop power supply is essential. Power is not usually supplied from the PLC input card. (Not saying it can't be, just that the I/O I deal with doesn't.)
It is possible to get fooled. For example, Micromotion does have a version of it's series 2700 flow transmitter that requires a 24dvc power connection but the signals are wired as 2-wire devices and require loop power. But this is pretty rare.
Note: L D[AR2,P#0.0] seems to be talking about 2 and 4 wire RTDs.
The 3-wire devices aikona is talking about can be considered to be 4-wire with the power supply com and the signal com shared. Usually found on cheaper devices.
Hopefully this helps rather than adds to the confusion...