Do you put a Karash Double Loop in the Bowline Family?
Make an educated guess...What does the following answer - that you have read, as you claim - does say, in a plain and CLEAR way ? Does it say that the Karash double loop IS NOT a bowline ?

If part of a knot is a bowlne, the whole knot remains a bowline - albeit a more complex one.
As part of the Karash loop is a bowline indeed, the whole double loop remains a bowline. Completing a knot can not erase a previously tied part of it, so, if a knot was a bowline, at one stage of its tying, it will remain a bowline, even after one adds some new parts on it.
what is the line of distinction between the Karash Double Loop and the Figure 8 Double Loop, such that one is a Bowline while the other is not?
The reason why the Karash double loop IS a bowline, is given in the answer above, that
now you have read, I hope !

The reason why the figure 8 Double loop IS NOT a bowline, is already repeated many times, but I would make just another attept : The figure 8 knot, tied on the eye leg of the standing part of a figure 8 Double loop, is not an unknot - it can not be removed after we remove the segment of the tail that goes through it.
No knot-that-can-be-fully-untied-with-the-removal-of-the-tail(s) off the standing part(s) = no bowline.
After a sailor has removed the tail from the eye leg of the standing part, he wants the bowline to turn onto the unknot immediatelly, so it will not run the danger to be caught somewhere, as the ship leaves the dock. So, even before the end of the line exits through the mooring ring, for example, the bowline should have been untied completely. If you are left with a figure 8. knot on your mooring line, you will probably forced to be an armchair only knot tyer, very soon ! 
Make an educated guess...What does the proceeding answer - that you have read, as you claim - does say, in a plain and CLEAR way ? Does it say that the figure 8 loop IS a bowline ?

it is still unclear to me where the line of distinction is.
Let me help you
here a little bit, because THAT IS the
most difficult point, indeed...

The Karash double loop IS a bowline, while the figure 8 double loop IS NOT a bowline !
That is a somehow CLEAR line of distinction, to me...
Of course, you can find many other, secondary reasons why two different knots are different, I suppose... I would be nterested to learn them, too, however insignificant they might be, because
any difference of two different entities can reveal something essential from the deeper identity of each of them.
Or maybe by default you also put the Figure 8 Double Loop in the Bowline Family?
Did I say that you should have read my answers by now ? Well, this question makes me wonder if I should really be
so sure !

If you could could only listen and see my
"rhetoric and hand waving" to
myself now...
Knot4u, please, let us be liberated, at least for some time, from this sterile exchange of opinions ( among other things...

) about this Karash-double-whatever, that I, personally, do not find such a clever knot... In my reply to a thread that you, too, have participated, (1), I have published the pictures of a particular dressing of a ,double loop that might be of some interest to you. Let us talk about double loops then, a very interesting and vast subject !
1)
http://igkt.net/sm/index.php?topic=3046.0