Two phase? Well it is a bit more complicated than that. And it is embedded in tradition.

Three phase is not three phase because it uses three wires. It is three phase because the sine waves have THREE different phase angles. So the three wires are a consequence of that, not a defining factor. In fact, if there was no fourth conductor (wire or otherwise) that defined the ground level that you are measuring the three phases from, then you could not measure those three phase angles. They must be measured from some reference point. So a three phase system, by necessity has four conductors.

OK, so what is two phase. Simply stated it is a system with two AC Voltages that, when measured from a ground conductor, have TWO different phase angles. Four phase would have four such AC Voltages, five phase would have five, six phase would have six, etc. Simply stated, that is what is meant by a number of phases. Please note that I did not say that the phase angles measured between the various phases must be the same. They do NOT need to be the same. Thus, a three phase system normally has equal phase angles of 120, 120, and 120. But other combinations that add up to 360 degrees would also be three phases: example: 100, 120, and 140. That example would not be common, but it could not be called two phase or four phase or any other number of phases other than three. Other examples would be possible: 10, 40, 310 or 25, 35, 300 or any combination of three numbers that add up to 360. All would be three phase systems.

But two phase? What is two phase? From a general point of view, two phase is simply any system that has two AC Voltages that have different phase angles when measured from a stated ground reference. HOWEVER there is tradition. Somewhere in our past, there was a system that used TWO phases that were separated by 90 and 270 degrees. This probably came about because the mechanical generator that was used had two coils that were oriented 90 degrees to each other. That is the simplest way to arrange two coils on a rotor and it is certainly how any designer would do it. That IS a two phase system. No arguement, but I did use the preposition "a" not "the". Since it was the only two phase system at that time, it was simply known as "two phase" just as 120, 120, 120 three phase was called simply three phase.

Then along came distribution to the homes and small shops and offices. The vast majority of these did not need three phase so only one phase of the three phases that are generated and distributed nationwide is carried to a local group of homes. The three phase power comes to your neighborhood, but your block only gets ONE of those three. So it was called SINGLE or ONE phase. Sounds logical. Here comes the rub. That SINGLE phase is distributed with a SINGLE transformer on a pole near you at a 230 VAC level. Someone must have thought that this was kind of high and wanted to lower it, perhaps for safety. So they came up with the idea of a center tap on that pole transformer. The single 230 VAC phase became TWO 115 VAC lines that were 180 degrees apart. So, is that split phase still a SINGLE phase or is it now two phases? The only difference is in terminology and the history of the system in the US. Since there was a prior two phase system (the 90, 270 one) some wise or perhaps not so wise engineer choose to call it a split phase system. The 115-0-115 Volt split phase system that we use in the US is certainly two phases by the basic definition of phases. But by common usage, it is not called that. It is commonly referred to as single phase and not so commonly as split phase.

I agree that there is no limit to the confusion that this causes. Frankly, the terminology is not consistent.