Sati (acquisition of)
Samādhi (establishment in)
As far as the four courses to attain the acquisition (of citta) [the cattāro satipaṭṭhānā] are concerned; they are a connected series of developments, and a route along which someone travels to reach its own citta, (that is to say, to reach the ("fine material" ) nāmarūpa nidāna) via the help of yoniso manasikara.
Please refer to this visual aid:
Yoniso manasikara has very little to do with the neo-pseudo-buddhist western concept of "mindfulness" (attention/concentration-like).
Yoniso manasikara is about turning/directing (√ कृ kṛ) the mano, towards the origin.
That is to say towards the nāmarūpa nidāna.
Notice the two definitions of nāmarūpa in the visual aid. The SA 298 definition, and the SN 12.2 definition.
When a satta (man/woman) wants to avoid to be within the context of the latter definition (that leads to mano-sañ-cetanā and the maintenance of consciousness), he/she has to yoniso "manasikarize" towards the context of the former definition. That is to say, towards the nāma-rūpa link in paṭiccasamuppāda - bypassing in the process, the contact (phassa) with the external field of sensory experience (bāhirāni āyatanāni).
This is what Buddha taught Bāhiya, as recorded in the Udāna (Ud 1.10), or to Mālunkyaputta in SN 35.95.
That is to say that, once one tries to reach back into the nāmarūpa nidāna (causal link), ante the saḷāyatana nidāna, without involving the sensory contact with the external fields of sensory experience; then one is neither "by that" or "in that" external fields of sensory experience (bāhirāni āyatanāni) - nor (much) "in" the internal fields of experience (ajjhattikāni āyatanāni) anymore, depending on how close one is to run aground the nāmarūpa nidāna - nor "beyond"; that is to say, within the all shebang of the upādānakhandhas, taṇhā, ... manosañcetanā, etc. - nor in between the two; that is to say in sense-consciousness.
The external fields of sensory experience (bāhirāni āyatanāni) is what is defined in the suttas, as what one considers "mine". While the nāmarūpa link before the saḷāyatana link, is considered as what one considers "I" (see SN 22.89 & SN 22.47 for that matter).
To yoniso "manasikarize" , with the internal field of sensory experience (ajjattikani āyatanāni), using mano (manasikara); directly towards the nāmarūpa link - allows one to pick the attribute (the sign) of his/her own citta (SN 47.8).
The process of running back aground the nāmarūpa nidāna, corresponds to entering second Jhāna or the 9th step of Ānāpānasati.