[snip]

You start off with the wrong assumption that because one particular system
of two phase was called two phase, that means that defines what two phase
means. To do this right, you first need to define what an N phase power
service would look like. Hint: It's not limited to 90 degrees phase
difference. I have defined it in the past, no one else has.

So, here are your questions. Let's take your second example of what you
say was the old two phase power, ie 90 deg phase difference, three wires with
a common return. I changed the phase difference to 70 deg by rotating
one of the windings on the generator. Are there
still two phases there? Now I change it to 179 deg, are there still
two phases there? I change it to 181, are there still two phases there?
I change it to 180 deg, are there still two phases
there? And how is the latter any electrically different than the
3 wire 240/120V service going into a home? Describe how I could tell
from the panel in your house which of the two I had, how they are
electrically different, how they behave differently?

This is based on semantics without definitions and reliance on what
something was historically, not electrical engineering. Would I call
240/120V, two phase? No, because it's not commonly referred to as that,
but that does not change the fact as to what's actually there, you
have two 120V sources that are 180 deg out of phase with each other.

Whether you have 1 phase or 2 depends on the reference point, either the
middle of the (center tapped) transformer secondary or one end. It seems
normal to use the point that's grounded.

120V, 120V (2 phases, 180 deg. apart))

or

120V, 240V (same phase)

Some people seem to be confusing this with the single phase at the
transformer primary.

--
106 days until the winter celebration (Wed, Dec 25, 2019 12:00:00 AM for
1 day).

"God has done nothing for men and women except to scare them out of
their wits." [Lemuel K. Washburn, _Is The Bible Worth Reading And Other
Essays_]