light-years and sound-seconds as units of distance associating time
and a reference speed
To get the gist of it take another situation, very frequent on our
Earth. No relativity needed, only shelter.
When there is a storm, you sometimes see lightnings, with no other
noise than the rain. You look at your watch, and after 20 seconds you
hear the thunder. Then you say (in my metric country), this storm is
seven kilometers away.
Actually, you are considering that for the purpose of this problem,
lights travels instantly (which is an acceptable approximation
here). So you know the exact time of the lightning event. But the time
taken by sound to propagate is much longer. When you hear the thunder
20 seconds later you think: ahah ... this event took place 20
sound-seconds away. A sound-second being the distance covered by sound
in 1 second, which is approximately 350 meters.
The sound you observe is from an event that occured 20 seconds earlier
at a distance of 20 sound-second, which is approximately 7 kilometers.
The sound-second is my just invented unit of distance for storm lover
(it may have been invented previously :-)
There is nothing more fancy about light years.
The main difference in the storm example is that you know the time
difference (how long ago the lightning event occurred) and the speed
of sound, and you compute from it the distance of the event in the
unit sound-seconds, which you translate in meters.
In the astronomical case you know the distance in meters, mesured by
some astronomical techniques, then you convert it in light-years, and
that tells you how long ago the event took place.
As for the sentence you quote, it is just nonsense. The best you can
say is "If we oberve them today 10 light years away, that means they
existed 10 years in our past". As for the present, if you want to be
very precise, you are not seeing it at all, because it always takes
time to reach your senses. Sorry for the bad news, but all you can
know is already past. In that sense the second part of your quote is
Actually, if the sun were to disappear, you would not know it for another 8.3 minutes, as it takes light that much time to cover the distance. We are not seing the present very far away is an understatement.
Regarding photons and relativity, I am not sure what you mean. But it
is probably not needed to answer your question.