Had a brief glance. Well-writting, but unfortunately with more wrong ideas of jhana. You just have my word for that, though So let’s look at the Pali, as that is what you are asking about.
The translation “concentration” for samadhi definitely isn’t really very accurate. So it’s good to get away from that. I’m not too happy about “collected”, though.
The literal meaning of samadhi is “brought (dhi) together (sam)”. You could say bringing things together is collecting them, but in English “to be collected” means something very different than “collecting things”, so it’s a bit misleading, imo, to translate samadhi that way. Because “to be collected” means to be calm, while samadhi has much deeper implications than that.
To me samadhi means “brought together” in the sense of bringing to one place. This is first of all how the word is used in a non-meditative context. A turtle “brings together” (“samadhi-s”) his limbs and head under it’s shell. (SN35.240) Or when you light a fire you bring together (“you samadhi”) the burning kindle with the wood. And this is also how samadhi is defined in a meditative context: as ekodibhava and citassa ekaggata, both having the idea of “unity” (eka) in there. (E.g. MN44)
So one idea behind samadhi, which I adhere to, is that there is just one (eka) sense going on in jhana, which is the mind. You “bring together”, in a sense, all your awareness under the mind, and lose all awareness of sounds and body. Also the sense of “self versus object” disappears, and the experience is “unified” in a sense that there is no feeling of “meditation and me the meditator” but just the meditatio nitself. (Which, tangentially, is super weird, but exactly why the jhanas can lead to insight into anatta, the absence of a self.) And in the second jhana, which is said to be “born of samadhi”, also the movement of the mind ceases, so here it means oneness in the sense of stability of the object and awareness, which doesn’t move.
As to the word “jhana”, it’s true that it can in some rather rare contexts mean “meditation” in a general sense. However, when talking about the jhanas in context of samma samadhi, they are not. Here the jhanas are obviously numbered (as the first, second, third, fouth), and they are always described with very specific formulas, where they always follow one another in a definite sequence. So we are obviously talking about very specific states. It no longer means meditation in general, but certain definite states. Context is important here.
On a more general note, superficial ideas about jhanas such as these perhaps may seem to make some sense from a practical perspective, probably because they are more “accessible”, but don’t forget that in the suttas even great arahants-to-be like Mogallana had trouble with accessing the jhanas. Also, the jhanas are on the same level of “attainment” as psychic powers, such as reading minds, remembering past lives, astral projection, and such, and the stages of enlightenment, too: all these very deep and non-ordinary things that require a lot of practice, they are all called extraordinary superhuman states. Again, together with the jhanas. So if someone has jhanas, they also will have these kind of powers available, according to the suttas.
Also, in the suttas the jhanas are described exactly the same for the Buddha as for anybody else. That means that when you enter jhana, your mind is exactly like the Buddha’s would be in a jhana. I think that gives you an idea of how high the bar is. All sense of self and delusion are gone (temporarily).
And that’s why as monks we are not allowed to tell lay people we have attained such things. If jhanas were some ordinary easy-to-reach state of “collected meditation” this wouldn’t make sense, because just about everybody could do it. There wouldn’t be much bragging rights involved. And it wouldn’t be extraordinary. Reality is, however, that jhanas are quite rare.
Though it’s well-intended, from what I’ve read I find this writing unfortunate as it’ll lead people the wrong way. I don’t mind saying that.
Sorry, I went on a bit of a rant there that went beyond just the translations of the words. But again, context is important. Hope I was of any help.