Understanding chain of narration

Question

In the chain of narration (sanad), it is often written in English:

1. Some narrator in the authority of some other narrator
2. Some narrator informed some other narrator
3. Some narrator related before some other narrator

I wish to understand the meaning of each of this statements.

My questions are -

1. Do the said English phrases have the same meaning (maybe very little difference)?
2. If not, what is the implication of each? a. Especially 'Some narrator related before some other narrator' sounds a bit odd. What does 'related before' mean? b. What does 'in the authority of' mean? c. How did some narrator 'inform' some other narrator? Orally? By letter? Sent a messenger?

Example: "Shams al-Din related before us; he said:" from Ibn Sa'ad.

The Shaykh, the Imam, the Hafiz, the most learned, the well versed in genealogies, Sharaf al-Din (the glory of religion) Abu Muhammad Abd al-Mumin Ibn Khalaf Ibn Abi al-Hasan al-Dimyati (may God show him mercy) informed us, and I was hearing; he said: The Shaykh, the Imam, the Muhaddith of Syria and the trusted Shams al-Din Abu al-Hajjaj Yusuf Ibn Khalil Ibn Abd Allah al-Dimashqi related before us; he said: Abu Muhammad Abd Allah Ibn Dahbal Ibn Ali Ibn Karah related before us; he said: Al-qadi Abu Bakr Muhammad Ibn Abd al-Baqi Ibn Muhammad Ibn Abd Allah al-Ansari related before us; he said: Abu Muhammad al-Hassan Ibn Ali Ibn Muhammad Ibn al-Hasan Ibn Abd Allah al-Jawhari narrated on the authority of Abu Umar Muhammad Ibn al-Abbas Ibn Muhammad Ibn Zakariyya Ibn Yahya Ibn Mu'adh Ibn Hayyawayh al-Khazzaz (silk merchant), from (i.e. on the authority of) Abu al-Hasan Ahmad Ibn Ma'ruf Ibn Bishr Ibn Musa al-Khashshab (timber merchant); from (i.e. on the authority of) Abu Muhammad al-Harith Ibn Muhammad Ibn Abi Usamah al-Tamimi from (i.e. on the authority of) Abu `Adb Allah Muhammad Ibn Sa'd Ibn Muni (may God show him mercy); he (i.e. Ibn Sa'd) said:

Also look at the English translation of the first paragraph of this page - https://www.bukhari.tv/sanad/ :

A reading on the authority of his sheikh, the knowledgeable and beloved Abd al-Qadir bin Ahmad al-Saqqaf, and he narrated it on the authority of his father, Imam Ahmad bin Abd al-Rahman al-Saqqaf, who narrated it. A reading on the authority of his sheikh, Imam Ali bin Muhammad al-Habashi, who narrated it on the authority of his sheikh, Imam Aidaroos bin Omar al-Habashi, and it is the Musnad of Hadhramaut and his name is proven. “Nahhat al-Fattah al-Fatir fi the chains of transmission of the great masters,” in which he mentioned its chain of transmission in his narrations, on the authority of his sheikh, Imam Abdullah bin Ahmad Basudan, who said: I narrated it on the authority of our sheikh, Sayyed Imam Omar bin Abdul Rahman al-Bar, on the authority of our sheikh and his sheikh, Sayyid al-Baqiyya, Hamid bin Omar bin Hamid Al Abi Alawi. On the authority of his beloved sheikh Abd al-Rahman bin Abdullah Belfaqih, on the authority of his sheikh al-Musnad al-Hasan bin Ali al-Ujaimi and Sheikh Ahmad bin Muhammad al-Mathili, on the authority of their sheikh, the hafiz of his time, Muhammad ibn Ala al-Din al-Babli, and he narrated it on the authority of Abu al-Naja Salem bin Muhammad al-Samhouri, on the authority of the conclusion of the hadith narrator, the star Muhammad ibn Ahmed Al-Ghaiti, on the authority of Sheikh Al-Islam Zakaria bin Muhammad Al-Ansari, on the authority of the Commander of the Faithful in Hadith, the Hafiz Ahmed bin Ali bin Hajar Al-Asqalani, on the authority of his sheikh Ibrahim bin Ahmed Al-Tanukhi and Abdul Rahim bin Razin Al-Hamawi, on the authority of Abi Al-Fadl Ahmed bin Abi Talib Al-Hajjar, on the authority of Al-Hussein Al-Mubarak Al-Zubaidi, on the authority of Abu Al-Waqt Abdul Awal bin Issa Al-Harawi, on the authority of Abu Al-Hasan Abdul Rahman bin Al-Muzaffar Al-Daoudi, on the authority of Abu Muhammad Abdullah bin Ahmed Al-Sarkhasi, on the authority of Abu Abdullah bin Muhammad bin Yusuf bin Matar Al-Farbari, on the authority of the Commander of the Faithful in Hadith, Abu Abdullah Muhammad bin Ismail Al-Bukhari May God Almighty have mercy on him....

Answer 1

What you are mainly asking for or might be a reason for your confusion are statements of scholar on how they got the information from their teachers. In such cases, an English translation by tools such as Google Translate usually creates even more confusion due to a literal translation of terms into "before us" or alike.
Further, be aware that sometimes scholars add information about a narrator or the exact session they heard or noted a narration at this information is then transmitted to their audience and their audience and so on.

For starters and to give you an example: let's at least start a detailed translation of the chain of transmission of (Al-Habib) 'Ali al-Jifri:
(1) in the following refers to the translation in your post,
(2) the explanation (if necessary),
I'd add here and there further comments to -hopefully- make things clearer:

قراءة عن شيخه العارف الحبيب عبد القادر بن أحمد السقاف ،
(1) A reading on the authority of his sheikh, the knowledgeable and beloved Abd al-Qadir bin Ahmad al-Saqqaf,
(2) reading ^{(refers to al-Habib 'Ali al-Jifri)} in front of his sheikh ^{(or while his sheikh was listening)} the knowledgeable al-Habib 'Abdul Qadir ibn Ahmad as-Saqqaf.

This sentence means that 'Ali al-Jafri either recited from his memory or while reading from a book/script (I'd assume the first to be more correct), while his teacher was listening.
there are mainly two ways a Muslim scholar would hold his lesson:

• Scholar reads from a book and explains or asks his students to check if they can follow the lesson. This is the way I have witnessed and really enjoyed in Maghreb countries, especially for subjects that don't require correct memorization like Fiqh, Arabic language, Balagha (Eloquence), Tafsir, and so on. A variation is also that a scholar recites out of his memory this was applied in history and sira topics by a scholar I've witnessed.
• Scholar leaves a student reading while he corrects his spelling mistakes etc. and explains. This is very common in the Arabic peninsula and is mostly used when the topic needs memorization like hadith.

So for hadith memorization, there are two options:

• Student reads in front of the teacher who may correct some mistakes and when he memorizes, gets checked (peer review) by the latter.
• Teacher recites in front of students, students memorize and a later peer review is done to get his teacher's approval.

See also:
Difference between ﺃﺧﺒﺮﻧﺎ & ﺣﺪﺛﻨﺎ

and
What is the difference between the different formulations used in describing how a hadith was transmitted?

وهو يرويه قراءة عن أبيه الإمام أحمد بن عبد الرحمن السقاف ، (1) and he narrated it on the authority of his father, Imam Ahmad bin Abd al-Rahman al-Saqqaf,

This looks clear to me.

الذي يرويه قراءة عن شيخه الإمام علي بن محمد الحبشي الذي يرويه ،
(1) who narrated it. A reading on the authority of his sheikh, Imam Ali bin Muhammad al-Habashi
(2) who narrated it by reading it from his sheikh, ...

This means he memorized his narration by reading it in front of his teacher from a script (which could be his own or his teacher's script) or from his memorization and got approval for that.

عن شيخه الإمام عيدروس بن عمر الحبشي ، وهو مسند حضرموت وله ثبت اسمه “منحة الفتاح الفاطر في< أسانيد السادة الأكابر” ، ذكر فيه أسانيده في مروياته ،

(1) who narrated it on the authority of his sheikh, Imam Aidaroos ibn Omar al-Habashi, and it is the Musnad of Hadhramaut and his name is proven. “Nahhat al-Fattah al-Fatir fi the chains of transmission of the great masters,” in which he mentioned its chain of transmission
(2)who narrated it on the authority of his sheikh, Imam Aidaroos ibn Omar al-Habashi, who was ^{(maybe known as)} the Musnad^(*) of Hadharamout and he has a book ^{(or composition)} called "Minhat al-Fattah al-Fatir fi Asaaneedi as-Sadah al-Kibar" ^{(translation: The gift of The Reliever (and) Creator on the chains of transmission of the great masters(Could also be a reference to Sadah: plural of Sayyid)")}, in which he mentioned his chains of transmission

^(*) Musnad could also be similar to Habib a specific honorific/title in the Yemeni circle of sufis or something like that.

Here one can see how a tool can change the meaning by wrong or literal translation without background knowledge!

In my humble opinion going on with the rest of the transmission chain is too much ado for nothing since it is rather a chain: x who narrated from y ...
However, in some cases, it is mentioned that the student (sheikh Imam Abdullah bin Ahmad Basudan) narrated from the teacher (sheikh, Sayyed Imam Omar ibn Abdul Rahman al-Baar) and his teacher's teacher (sheikh, Sayyid al-Baqiyya, Hamid ibn Omar ibn Hamid Al Abi Alawi) or from two teacher's (sheikh al-Musnad al-Hasan bin Ali al-Ujaimi and Sheikh Ahmad ibn Muhammad al-Mathili) who narrated it from their teacher (sheikh, the hafiz of his time, Muhammad ibn Ala al-Din al-Babli).

عن شيخه الإمام عبد الله بن أحمد باسودان قال : أرويه عن شيخنا السيد الإمام عمر بن عبد الرحمن البار ، عن شيخنا وشيخه السيد البقية حامد بن عمر بن حامد آل أبي علوي، عن شيخه الحبيب عبد الرحمن بن عبد الله بلفقيه ، عن شيخه المسند الحسن بن علي العُجيمي والشيخ أحمد بن محمد المثلي ، عن شيخهما حافظ عصره محمد بن علاء الدين البابلي ، وهو يرويه عن أبي النجا سالم بن محمد السمهوري ، عن خاتمة الحفاظ النجم محمد بن أحمد الغيطي ، عن شيخ الإسلام زكريا بن محمد الأنصاري ، عن أمير المؤمنين في الحديث الحافظ أحمد بن علي بن حجر العسقلاني ، عن شيخه إبراهيم بن أحمد التنوخي وعبد الرحيم بن رزين الحموي ، عن أبي الفضل أحمد بن أبي طالب الحجار ، عن الحسين المبارك الزبيدي عن أبي الوقت عبد الأول بن عيسى الهروي ، عن أبي الحسن عبد الرحمن بن المظفر الداودي ، عن أبي محمد عبد الله بن أحمد السرخسي ، عن أبي عبد الله بن محمد بن يوسف بن مطر الفربري ، عن أمير المؤمنين في الحديث أبي عبد الله محمد بن إسماعيل البخاري رحمه الله تعالى …..

Shamsu a-Dyn related before us

This could simply mean that the teacher narrated it in front of his students as mentioned above. But this is a guess since your quote is a translation of a so far unknown text. Once this text is clarified I could give a better answer.