These discussions seem to me to make my point. Most everyone seems to have the correct concepts in mind. It just boils down to how we describe them. In other words: "We agree on what it is but what do we call it?" Sometimes you have to describe something in several different ways, all of which can be correct, to make it understandable to some who does not understand it. One idea I used in describing leading and lagging phase concepts is riders on a merry-go-round. If two are exactly opposite (180 degrees apart) , who is leading? Maybe it would be clearer if we kept phase and polarity separate. For fun, shift from sine waves to pulses to see how you can confuse the issue.
The power issue is also important to understanding. It took a long time for me to see how 3 phases at 120 degrees provided more uniform power than 2 phases at 90 degrees. Of course the 3 phase system provides power peaks every 60 degrees and the 2 phase system only every 90 degrees!! That can be clear as mud for a student. I also think it's important to keep in mind that a voltage never appears on or at 1 conductor, but only between 2. In a 3 wire system it is correct to refer to phase A, B, or C current but the voltages have to be A-B, B-C, and C-A. It often helps if we are clear whether we are referring to voltage, current, or power.
Don Young