For some reason, DN 7 is simply a repeated portion of DN 6. I have no evidence for this, but I suspect that the portion in question may have first been a stand-alone sutta, later inserted into DN 6 for some reason, rather than this portion being extracted from DN 6 and then made a stand-alone sutta. It seems completely out of place in DN 6.
In any case, I have decided to forego creating a separate page for DN 7. This page will serve as the synopsis for both DN 6 & 7.
This story takes place in the city of Vesālī, capital of the Vajjian Republic. The Buddha and his monks were staying at a roofed building inside the Great Forest. There were also many Brahmins from the kingdoms of Kosala and Magadha who were staying in Vesālī, acting as emissaries on business.
These Brahmins heard rumors about the Buddha and his reputation as a fully-enlightened teacher of gods and men, much like what happened in some of the previous suttas. They decided to go and see him. At the time, the Venerable Nāgita Kassapa was the Buddha's attendant, and the Brahmins met him in the forest. "Venerable Nāgita, where might we find Master Gautama?"
"This is not an appropriate time, Brahmins." answered the monk. "The Buddha is on retreat right now." The Brahmins talked with one another and reached the conclusion that they should simply wait until they could see the Buddha. They sat off to the side, determined to stay as long as it took.
At this time, a second group of men arrived in the Great Forest, also hoping to meet with the Buddha. This group came from the kingdom of Licchavi, led by a man named Otthaddha Mahāli. Nāgita told them the same thing he told the Brahmins, and they also resolved to sit and wait for as long as was necessary to meet the Buddha.
Upon seeing this, a novice monk named Sīha - who was highly-respected, despite his rank - approached Nāgita, bowed, and said, "Venerable Kassapa, both of these groups have come to see the Lord. It would be good for them to be able to see him." Nāgita replied, "Very well. Go and tell the Lord yourself."
The novice did so, and the Buddha had him prepare a seat. When everything was ready, the Brahmins approached, exchanged polite greetings, and sat to the side. The Licchavis approached with a higher degree of reverence, bowing before sitting.
Otthaddha took the lead. "Master Gautama," he said, "I was recently approached by Sunakkhatta, my fellow countryman and a disciple of yours. He said he has followed you for nearly 3 years, and that he has seen beautiful heavenly sights. However, he has not heard any such heavenly sounds. Do these sorts of sounds exist, and Sunakkhatta simply can’t hear them? Or do they not exist?”
"They exist, Mahāli." answered the Buddha. "He simply cannot hear them." In response, Otthaddha asked, "Why is it that he cannot hear heavenly sounds, despite being able to see heavenly sights?"
The Buddha began explaining how monks might have different experiences depending on the way they develop samādhi. "A monk might face the east, developing one-sided samādhi—entering into one particular state of concentration—and as a result, he will see heavenly sights, but fail to hear heavenly sounds. A monk might face every direction, but if they only develop this one-sided samādhi, they will only see heavenly sights, failing to hear heavenly sounds."
He continued. "We can consider the opposite case, too. A monk might face the east, or every direction—but if they only develop a one-sided samādhi, they might only hear heavenly sounds, failing to see the heavenly sights. However, if a monk develops a two-sided samādhi—entering into a more comprehensive state of concentration—he can see heavenly sights and hear heavenly sounds too. Sunakkhata has only developed a one-sided samādhi."2
Otthaddha asked, “Have your monks joined the order in order to attain this two-sided samādhi?” The Buddha responded, "No, Mahāli. There are other things, far more important, which motivate my monks." Otthaddha asked the Buddha to explain these more important goals.
"First, there is the state of Stream-Enterer. This is achieved when a monk abandons the first three of the lower fetters - namely: belief in a self, doubt, and attachment to rites and rituals. Having achieved this state, he will never again be reborn in the lower realms. He has irreversibly set himself upon the path to enlightenment. The attainment of this state is more important than developing the two-sided samādhi."
"Secondly, there is the state of the Once-Returner. This is achieved when a monk abandons the first three of the lower fetters, and reduces the strength of his greed, hatred, and delusion. He will only be born into this world one last time, and in that lifetime, he will attain enlightenment. The attainment of this state is more important than developing the two-sided samādhi."
Thirdly, there is the state of the Non-Returner. This is achieved when a monk abandons the five lower fetters - the three above, as well as sensual desire and ill-will. He will be reborn spontaneously3 in one of the Pure Abodes. In that world, he will attain enlightenment. The attainment of this state is more important than developing the two-sided samādhi."
Finally, there is the state of the Arahant. This is achieved when a monk abandons all of the fetters - the five lower fetters, as well as the ten higher fetters, namely: desire for material existence, desire for immaterial existence, conceit, restlessness, and ignorance.4 He abandons the corruptions5 through direct insight and wisdom, and attains enlightenment in this world, in this lifetime. The attainment of this state is more important than developing the two-sided samādhi."
Otthaddha asked, "Is there a practice which leads to the realization of these states?" The Buddha responded, "Yes, there is." Otthaddha asked the Buddha to elaborate.
"Mahāli," the Buddha said, "I have taught the Noble Eightfold Path: Right View, Right Thought, Right Speech, Right Action, Right Livelihood, Right Effort, Right Mindfulness, Right Concentration. This is the practice which leads to the realization of those things, which are better than the two-fold samādhi and seeing heavenly sights orhearing heavenly sounds.”
The sutta suddenly shifts to the Buddha recounting a conversation he once held with two ascetics regarding the soul and the body.
This section also makes up the entirety of DN 7, the Jāliya Sutta. The only difference seems to be that in DN 6, the Buddha told the story personally and addressed Mahāli by name, while in DN 7 the story is told in a narrative voice (traditionally, this is understood as the voice of Ānanda recounting the sermons), and there is no indication that Mahāli was present at all. Otherwise, the content is exactly the same.
“Once, Mahāli, I was staying in the monastery at Ghosita Park in Kosambi.6 Two ascetics visited me—the wanderer Mundiya [or Mandissa], and Jāliya, who was the student of Dārupattika, the wooden-bowl ascetic. They wanted to know if the soul7 and the body are the same thing, or if they are two separate things.”
The sutta presents the Sīlakkhandavagga Pericope as the Buddha’s response. The first section begins with the appearance of a Tathāgata, up to the completion of the first jhāna. After this, the Buddha asked the two ascetics, "Would it be proper for someone who has achieved this to ask such a question about the soul and the body?" The two ascetics answered, "Yes, it would." The Buddha countered, "Well, I have achieved this, and I do not say that the soul and the body are the same thing - nor do I say they are two separate things."
This back-and-forth exchange repeats for the rest of the Sīlakkhandavagga Pericope, with interruptions to show the Buddha asking the two ascetics if it is appropriate for someone who has achieved those things to ask the question about the soul and the body. In each case, they answered in the affirmative, and he responded with the above rebuttal.
Both suttas conclude after this point.
In DN 6, the conclusion states that Otthaddha the Licchavi rejoiced at the Buddha's words. In D7, the conclusion states that Mundiya and Jāliya rejoiced. In DN 6, the reaction of the two ascetics is not included as part of the story. Furthermore, neither sutta mentions any of these individuals converting, as many of these suttas in the Sīlakkhandhavagga do.
As far as I'm aware, there is no parallel text for DN 6 or 7 in the Chinese Canon.
 I have only come across one source which seems to have notes on these terms: "Early Buddhist Meditation: The Four Jhanas as the Actualization of Insight" by Keren Arbel. Unfortunately, the relevant footnotes are not in any freely available version I can access, and this book is behind an expensive paywall. Right now, I can't justify paying for a digital book rental just to check two footnotes. If I ever liberate this knowledge from behind this paywall, I will update this page.
In any case, these states of samādhi seem to be two of the sorts of attainments produced from concentration which do not ultimately lead to enlightenment. As such, they are not considered terribly important - they're better seen as a byproduct of practice than a goal to be pursued.
 I have left out a great deal of repetition in this section. Walshe points out that this degree of redundancy is extreme even for the Buddhist scriptures, already known for their repetitiveness. This is made more puzzling by the mundane nature of the lines being repeated. He raises the possibility that this is indicative of DN 6 being a late sutta. I believe this is reasonable, especially since I can’t seem to find a parallel for this sutta in the Chinese Canon. The issue of DN 6 and DN 7 containing the same text in two different suttas only strengthens my suspicion.
 This means that the birth will not be a result of sexual reproduction. The being will be born fully-formed.
 I have taken a couple liberties here, for the sake of convenience for the reader, and I want to be clear about that. In the sutta itself, the Buddha does not name what the fetters are, nor does he mention the higher fetters when discussing the state of the Arahant. These things are described elsewhere. I included them here for clarity.
 Sujato's translations often use the word "defilements" for "Āsava," when most translations use "defilements" to translate "kilesa" instead. I follow Walshe in using the word "corruption." This is something you should be aware of when you read translations of the suttas.
 The city of Kosambi was the capital of the Vaccha kingdom.
 The word for soul here is "jīvam," which is sometimes translated more technically as "life-principle." Even in the Buddha's time, the idea was a hot topic, with people debating whether or not the soul was "the self," whether or not there was a difference between the soul and the body, whether or not the soul was a material thing or something more subtle, etc. Ultimately, the Buddha considered these questions to be a complete waste of time. Navel-gazing about the nature of the soul won't lead you to enlightenment.