"Leo Lichtman" writes:
If there is ANY difference between two voltages of opposite
polarity, and two voltages 180 degrees out of phase, I can't find it
with an oscilloscope or in my mind. I don't think there is any
difference, but I may also be a pedant.

The relationship is not symmetrical.

It's relatively easy to generate two signals that are 180 degrees out
of phase, each of which can be measured relative to a common ground,
but show no voltage difference relative to each other. Think of two
relays (or light switches) which take turns turning a circuit on. You
can measure the output of either relays' contacts to ground, and see
the signal, but if you just connect from one relay to the other, you
get nothing.

In the case of a multi-tap transformer, the fact that it's a multi-tap
transformer is enough to make it a voltage issue rather than a phase
issue. Consider a transformer with ten taps. Are there ten phases?
Of course not, but there are ten (er, plus or minus a fence post)
voltages, which you can use in any [linear] combination, much like
putting batteries in series.

Now, if you had two identical transformers, and wired one backwards,
*then* you'd have a phase issue (still, though, no practical
difference). But like I said earlier, there's no practical difference
when we're talking about house current.

My primary motivation, other than to have some fun on a Friday, is to
keep people from confusing single-phase house current with the
original two-phase (4 wire, 90 degrees) AC invented by Tesla. This
2-phase was replaced with our current 3-phase (3 wire, 120 degrees)
power.