Confusion with interpreting leading and lagging concepts for given electrical quantities
And I think it is because we imagine the phasors are rotating counter clockwise and the reference point is the green line (positive x axis) ...


That is fine.


  ... the first phasor we encounter is A then B and then C.


No. If we are rotating counter-clockwise then A will be followed by C and then B. (Imagine A has just crossed the green line. Which one is next?)


  For these plot what is leading what? What should be the way of thinking here? Do we have to see the plots from the time zero or? (sic)


A simple way to do this is to decide which is going to be the reference signal. Usually we choose the voltage.



Figure 1. Leading or lagging? Voltage is blue. Current is yellow.

Next find the zero crossing point for the voltage. This is point (1) on the graph.

Then find the zero-cross for the current. This is point (2) on the graph.

Since these are within 180° of each other reading from left to right it makes sense to say that the voltage is leading the current. The lead is about 3 ms on a 20 ms cycle so that gives \$ \frac {3}{20}360 = 54° \$.

CIVIL

As an extra help, if you remember "C-I-V-I-L": in a Capacitor I leads V  but V leads I in an inductor. From this we can conclude that these voltage and current measurements were taken on an inductive load.



From the comments:


  Ok so we have to find zero crossing points for current and voltages where these points are less than 180 degrees apart from each other; then the point on the left side is the leading quantity. 


In power circuits the leading or lagging is 90° max so that's a good way to approach it. If you got a lag of 300° it would be much more sensible to convert this into a lead of 60°.


  That's cool we dont need the initial point for this; any steady state part of the plots work to interpret. 


Zero is an easy point to use. You could use the peak or trough also but the curve is flat (zero slope) at those points whereas it crosses the 0 line at a steep angle making it much more convenient to measure.