IMHO single phase center tap is _single phase_ service. rick hart made the essential point in the third post of this thread: the offset in the zero crossings (and by implication the offset of the entire sine wave).
The power delivered by a single phase system must of necessity drop to zero twice per AC cycle. This is true no matter how many taps you have on the system; with a properly wired transformer you could have 5 wire 480/360/240/120 single phase; but the power would still drop to zero twice per AC cycle. When you have a polyphase system, you can always draw power from at least some of the phases.
Part of the confusion comes from the fact that we use the term 'phase' to describe both the time displacement of the AC cycle, and also to describe the energized conductor itself.
In a residential 120/240V system, you have two legs, and by common usage each leg can be referred to as a 'phase'. But if you do this then you really should describe these as phase A and phase A' (read that as "A-prime"), since there is no offset in the zero crossings of the AC. (And in the silly 480...120 system above you would have A, A', A'', A'''' and the neutral
)
If you have a three phase center tapped delta, but look at only the two legs on the center transformer, then you still have _single_ phase power. There is no time offset between the two legs _as referenced to each other or the neutral_. The power delivered by these three terminals (the two hots and the neutral of the center tapped transformer) must fall to zero twice per cycle. It is only when you look at the voltages between all four of the taps on this delta transformer set that you have polyphase power.
If you have two legs and the neutral of a wye system, then even though you only have two legs and are using single phase equipment, this _is_ polyphase power. With a suitable load, connected to both legs and neutral, you could have power continuously delivered to the load; the zero crossings are offset between the various voltage pairs. You could even use these two legs with a suitable transformer set to re-derive the full three phase set.
-Jon