Thank you, thank you! I think the light is dawning! (I know that must be hard to believe, hehehe!)No, this is not correct. Look at the coordinates I gave for events. Alice, Bob, and Bob's light ray all start at (t, x, y) = (0, 0, 0) in Alice's frame. After 1 unit of time in Alice's frame--"time" meaning coordinate time in that frame--Alice is at event (1, 0, 0); Bob is at event (1, 0.6, 0); and Bob's light ray is at event (1, 0.6, 0.8). All three of these events have t = 1, i.e., they are at coordinate time 1. Alice's proper time between the two events is 1; Bob's is 0.8; and Bob's light ray has zero spacetime interval, which strictly speaking should not even be called its "proper time" since that term only applies to a timelike interval, not a null interval.
It is all down to semantics - understanding the words in the right way.
Let me see if I am getting it now. Proper time and coordinate time are not different ways of measuring the time. They are not measuring time against different time scales. They are descriptions of what is being measured. Proper time is the label applied to time measured on a worldline. Coordinate time is the label applied to times that are 'coordinated' by being measured in one frame by a single observer.
Yes, when Bob's light has travelled 0.8 light units in Bob's clock, in Bob's frame, Alice measures the light to have travelled 1 unit in Alice's frame, because the light has travelled 1 unit in her frame.None of these involve "measurement of time in another frame". They all involve coordinate times in Alice's frame.
It is not Alice reading Bob's measurement differently, it is Alice making her own measurement of the time in her frame.