Yes, Kokonoe is a particular cultivar of Japanese Five Needle Pine, also known as Japanese White Pine. There are two cultivars if JWP that can easily be propagated by airlayering: Kokonoe, and Zuisho. They are both considered to be dwarf varieties. Zuisho has slightly shorter needles. They both have shorter needles than most JWP. They can also be propagated by cuttings, but the “take rate” is very low, around 5%. They were discovered in Japan by Mr Suzuki in the 1930’s, I believe. Initially, they were propagated by grafting, but later, it was discovered they could be layered so they can grow on their own roots.
I have no idea if the third tree is a Kokonoe. It looks like one. I have one, and the foliage looks similiar.
As for grafts vs “on their own” roots....
Most JWP seedlings have poor foliage. Compared to the grafted JWP trees we see as bonsai, their foliage is longer, coarser, longer internodes, needles can be curly, or twisted or droopy. The grafted JWP were selected because of their superior foliage: short, tight tufts, blue, short internodes, straight fat needles, etc.
Therefore, when you compare a JWP “on its own roots” (I.e. a seedling) to a grafted JWP, the seedling looks really inferior. If the expectation is it would look like the grafted tree, it looks “weak” in comparison.
There are many grafted cultivars of JWP. I have a friend who have over 30 different grafted cultivars. I have 6 different cultivars, including Kokonoe and Zuisho.
The key to being successful with JWP is good draining soil, regardless of whether they are grafted or not. I give mine full sun. They don’t mind summer heat as long as they get a good winter chill. I don’t fertilize in the spring or early summer, but I do fertilize in the fall. If I were to fertilize in the growing season, I would get long needles and long internodes. I don’t want that. I wait until the sheaths have completely vanished, and the needles hardened off before I fertilize. I do give them some of Julian Adams “micronutrients” in the early spring. Here is one of my grafted JWP:
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The tree on the left is a Zuisho, by the way. You can see that it has shorter needles than the tall tree in the center.