Since we're going to be comparing measurements on two
coordinate systems in the next section, let's go to
our supply cabinet and get our yard-stick (which we
use to measure things in inches) and our meter-stick
(which we use to measure things in centimeters).

Here, I'm getting mine. Oh! Oh!

There's an ant on mine, and he ... she ... sure is
hanging on, right at the 3.5 inch mark of the yard-
stick.

Let's see if I can wave the stick around enough that
she'll let go. Nope.

However, before I gave up I waved the stick and the
ant 'all over the place".

Always, however, the ant was at the 3.5" mark on the 
yard-stick, and always 3.5" away from the end of the
stick, however far and wide I have transported her.

Neither of those 3.5" facts means very much. Of the
two, the distance aspect meant almost nothing. So
the distance was 3.5" from the end. So what? That
length, distance, was not in use. And only maybe
the ant might have been concerned with just what
location, 'just coordinate', on the stick she was
at.

Just so with x and t.

So, is the 3.5" reading just a coordinate? Or a
distance/length?  It's ambiguous in and of itself,
and really makes no difference what you say until
you try to make use of the number. 

Hey, my address is 5047 Newton Street. If you
are looking for me and you're at 4120 Newton, it
is helpful information, because it tells you which
direction to go.  Is that 'just coordinate'? 

Where it really becomes useful, perhaps, is in
telling you how far away I am. That's not just
a coordinate value, that's a distance, length,
interval.

However, it is subtracting 4120 from 5047 that 
tells you which direction and how far. It is only 
because both 5047 and 4120 are distances from the 
same point - ANY same point - that the result means 
anything.

My x - my yardstick reading - is always a distance
or length; it is impossible to be otherwise with
an honest, competently designed yardstick.

Whether or not its reading is of good use in some 
particular scientific formula depends on whether 
I put the zero end of the yardstick at some useful
place. As in the introduction, we should either
put it at the starting location/end, or use two
readings from it: (x-x0).