I agree, this is a thread about terminology, and 'phase' has many meanings.
One of the points made in the other thread was about the 'hexaphase' transformer. This is a set of 3 single phase coils, all with center taps, with the center taps joined to make a 'star'. Each of the output terminals of such a transformer is 60 degrees out of phase from the adjacent ones.
In the literature on high phase order motors they came up with a term to distinguish phase counting when you had 'phases' that were 180 degrees apart. They used 'hemi-phase'. So using that terminology the hexaphase transformer is a 3 phase transformer with 6 hemi-phases brought out.
Similarly a center tapped transformer is single phase with 2 hemiphases brought out.
Don't know if this helps or is just an extra word to be pedantic with
-Jon