Is Lorentz Transformation about the difference of coordinates or coordinates of itself?

I have seen different authorities talking about different interpretation of Lorentz transformation.

In his book 'Introduction to Classical Mechanics', David Morin states

We always talk about eh difference between coordinates of two events in spacetime. The actual value of any coordinate is irrelevant, because there is no preferred origin in any frame.

which made quiet a bit of sense to me considering that when I shift the origin, nothing really changes to one particular frame.

But when watching the video 'Fundamental of Physics I' by professor Shankar, who I suppose is academically stronger than Morin, he does not raise the issue at all and always use the single coordinate $x$ and $t$ to refer to events.

Is Lorentz transformation concerned with the difference in spacetime coordinates of events, or is using the coordinate of one event itself more preferred?

• Does it help to recognize that a coordinate represents a difference from the selected origin? – dmckee Aug 7 '15 at 1:27
• I see. But what about time coordinate? – Rescy_ Aug 7 '15 at 1:32
• A time coordinate is also a difference from some arbitrary zero time. – Bill N Aug 7 '15 at 1:46
• $dx^{'} =\gamma\left(dx-\upsilon dt\right)\Leftrightarrow \Delta x^{'} =\gamma\left(\Delta x-\upsilon \Delta t\right) \Leftrightarrow x^{'} =\gamma\left( x-\upsilon t\right)$ because of linearity – user82794 Aug 7 '15 at 5:22