Difference between ajjhosānaṁ and tanha;

Yes. You bring up an excellent point.

1. Most people just know the steps in PS. They have no idea what each step means. One can write a book on each step, especially for the “tanha paccaya upadana” step. That is where we get attached to an arammana and start accumulating kamma.

• This is when we start generating abhisankhara with “avijja paccaya sankhara” and initiate numerous PS cycles going round and round. 
• This sutta explains that step in a bit more detail. 
• I have discussed that in “Taṇhā Paccayā Upādāna – Critical Step in Paṭicca Samuppāda” and “Difference Between Tanhā and Upādāna.” I may have used different terms, but the idea is the same.
• Another relevant point is the importance of vaci sankhara, which is two-fold: (i) we first start thinking how to respond to an arammana, (ii) if our feelings get energized, we will start talking about it/asking about it, etc.

2. The following verses, starting with the verse you quoted, explain that:

“9.1Iti kho panetaṁ, ānanda, vedanaṁ paṭicca taṇhā, taṇhaṁ paṭicca pariyesanā, pariyesanaṁ paṭicca lābho, lābhaṁ paṭicca vinicchayo, vinicchayaṁ paṭicca chandarāgo, chandarāgaṁ paṭicca ajjhosānaṁ, ajjhosānaṁ paṭicca pariggaho, pariggahaṁ paṭicca macchariyaṁ, macchariyaṁ paṭicca ārakkho. 9.2Ārakkhādhikaraṇaṁ daṇḍādānasatthādānakalahaviggahavivādatuvaṁtuvaṁpesuññamusāvādā aneke pāpakā akusalā dhammā sambhavanti.

10.1‘Ārakkhādhikaraṇaṁ daṇḍādānasatthādānakalahaviggahavivādatuvaṁtuvaṁpesuññamusāvādā aneke pāpakā akusalā dhammā sambhavantī’ti iti kho panetaṁ vuttaṁ, tadānanda, imināpetaṁ pariyāyena veditabbaṁ, yathā ārakkhādhikaraṇaṁ daṇḍādānasatthādānakalahaviggahavivādatuvaṁtuvaṁpesuññamusāvādā aneke pāpakā akusalā dhammā sambhavanti. 10.2Ārakkho ca hi, ānanda, nābhavissa sabbena sabbaṁ sabbathā sabbaṁ kassaci kimhici, sabbaso ārakkhe asati ārakkhanirodhā api nu kho daṇḍādānasatthādānakalahaviggahavivādatuvaṁtuvaṁpesuññamusāvādā aneke pāpakā akusalā dhammā sambhaveyyun”ti?

3. The English translation there gives some idea. But those verses need to be explained in one’s own words.

“ajjhosānaṁ” means “really getting trapped in that arammana,” thinking, “should I do this or that? How can I get this for myself without others grabbing it?” , etc.

• This is also represented by vitakka/vicara. See “Vitakka, Vicāra, Savitakka, Savicāra, and Avitakka, Avicāra.”

Feel free to ask further questions after reading those posts.

pariyesanā – to investigate, analyze possibilities

pariggaho – to grab firmly, like an octopus grabbing with all eight feet

ārakkho – trying to keep for oneself; that is done with chandaraga and macchariya with the expectation of lābha.

In other words, you got close enough.

The following dictionary is useful (it still has some wrong translations too):

“Concise Pali-English Dictionary –A.P. Buddhadatta Mahathera“

Tanha and avijja go together. Both are wholly removed only at the Arahant stage.

• Vibhava tanha is the worst, the assumption of no rebirths. Then one would not be afraid of doing any immoral deed. That goes away at the Sotapanna stage.
• The strongest part of kama tanha is associated with kama raga and goes away at the Anagami stage.
• Bhava tanha is to “wish for” specific existences/titles/etc. The strongest component of an “unchanging soul” goes away at the Sotapanna stage. Cultivation of anariya jhana is included in bhava tanha.

“Kāma Tanhā, Bhava Tanhā, Vibhava Tanhā“

P.S. Yes the second post in #1 in my first comment is: “Icchā (Cravings) Lead to Upādāna and to Eventual Suffering“