If we wish to distinguish this bowline-like loop from other "similar" "proper" bowlines, we can say that it is a
crossing knot - based eyeknot - its nipping structure is not the "common" single nipping loop of the "common" bowline, but a crossing knot.
We all understand the difference between the bowline-like end-of-line loops based upon a single "proper" nipping loop knot, and those based upon a single crossing-knot. The problem is that, if we do not consider the end-of-line loops based upon a crossing-knot be included in the family of the bowlines, we run the danger to exclude the "Eskimo" bowlines as well- and this is something that the knot tying community is not ready to acept ( And, it is a debatable issue, because, when the angle of the two legs of the loop is greater than 120 degrees, the "Eskimo" bowline behaves exactly as the common bowline. See Reply#118, (1))
One possible escape is to narrow the definition of the crossing-knot based end-of-line loops, so that it will not include the "Eskimo" bowlines any more. Then, we can exclude those more narrowly defined crossing-knot loops from the family of bowlines, without throwing away the baby with the water - the "Eskimo" bowlines with the not-so-bowline-like crossing-knot loops. I know that this is a compromise, and as such, it will not satisfy 100% anybody ( except me - perhaps 
).
So, we can define as a "proper" crossing-knot loop a loop based upon a particular knot, where the standing part touches the nipping loop s rim for a second time, at a second point. Then, we can exclude this family of end-of-line loops from the family of bowlines, reduce the number of loops that are considered as bowlines, but at the same time leave the "Eskimo" bowline in its traditionally occupied place.
1) http://igkt.net/sm/index.php?topic=3233.msg19858#msg19858
Now, the interesting thing is that those knots, when capsized, can be transformed into "proper" bowlines, indeed - the "
coming and going" bowlines, where the nipping structure is now simpler ( the crossing knot has degenerated into a single "proper" nipping loop), while, at the same time, the collar structure has become more complex ( a double collar, around the standing end / tail pair and the eye legs pair). Moreover, the Jug Sling / Mike s fancy bend - based bowline is also a TIB knot. See :
http://igkt.net/sm/index.php?topic=4336.msg27161#msg27161
