Well, that's exactly where we differ.

The grounded leg of a corner grounded delta simply cannot be the 'same' as the grounded conductor of a center-tap delta. At the risk of repeating myself, I'll try to illustrate the difference with a few examples.

If you have a 3-phase motor on a center-tap system, the grounded conductor does not come into the picture at all. The motor will operate exactly the same whether the "neutral" is there, or not.

By way of contrast, that same motor on a corner grounded system absolutely needs to have that 'grounded' leg in order to operate. Swapping leads will change the directoin of rotation - something that doesn't work with single phase motors.

Then there's the fine matter of meter readings. Measure between any two legs, and you'll get full voltage - even though one of those legs will show "0" volts to ground.

These variations are probably why code language has been so turgid when it comes to discussing the 'neutral.'