What exactly is the relationship between samatha and samādhi? EBT sources?

thanks to Dmytro for referring this sutta,

The title of the sutta is suggestive “samādhi”. Taking into consideration MN 44’s definition of samadhi-khandha, that is in the 8aam (noble eightfold path), the 3 last factors of right vigor, right remembering, right undistractable-lucidity together form the undistractable-lucidity (samadhi) group (khandha).

So in the context of all the EBT passages on samatha and samadhi, it seems samatha is part of samadhi, not equivalent to it, as Ajahn Chah asserts (although based on some sutta passages it can be taken that way).

I will continue collecting passages to confirm this, but also note these two words that appear in the definition of samatha, saṇṭhapeti sannisādeti, (in part 2 of AN 4.94), also appear, along with “samadaham” and “ekodi”, as part of the instructions for attaining first and second jhana in MN 19, MN 20.

MN 122 explicitly tied to 4 jhānas

(thanissaro trans.)
♦ 188. “kathañc-ānanda, bhikkhu
And how does the monk
ajjhattameva cittaṃ
get the mind
saṇṭhapeti sannisādeti
steadied right within, settled,
ekodiṃ karoti samādahati?
unified, & concentrated?
idhānanda, bhikkhu vivicceva kāmehi vivicca akusalehi dhammehi ... pe ... paṭhamaṃ jhānaṃ upasampajja viharati ... pe ... dutiyaṃ jhānaṃ... tatiyaṃ jhānaṃ... catutthaṃ jhānaṃ upasampajja viharati.
There is the case where a monk—quite secluded from sensuality, secluded from unskillful qualities—enters & remains in the first jhāna… the second jhāna… the third jhāna… the fourth jhāna: purity of equanimity & mindfulness, neither-pleasure-nor-pain.
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