These are the first eight steps of Anapanasati, corresponding to the first jhana.
This is a correct translation.
As we have seen before, "sati" has two meanings:
1- from the Vedic smṛti, meaning "thinking upon" (~mindful). It can be being mindful of (thinking upon) the breath. Or being mindful of not letting the external akusala get in, etc.
2- from सति sati = साति sāti = gaining , obtaining , acquisition (RV.)
Ānāpānasati means therefore "the acquisition (of citta), through (mindful) breathing".
It takes both meanings (of sati), throughout the process of liberation.
Please, notice the relationship between sati (thinking upon) in Ānāpānasati, and Vitakka-Vicāra in the first jhana.
Vitakka is about thinking about the breath, and only the breath - (focusing on thinking only about it). (first and second step).
Vicāra is about knowing the particulars of both in & out breathes. (third step).
What is usually called "wisdom" (pañña) is "discerment".
Discernment between in & out breath - discernment between pīti & sukha - discernment between mano & citta(ssa).
Some working for the Mara's world; some for the Brahma's world; some for the Unborn.
In this world with its ..., māras, ... in this population with its ascetics.... (AN 5.30).
We are all possessed - more or less.
And what, bhikkhu, is inward rottenness? Here someone is immoral, one of evil character, of impure and suspect behaviour, secretive in his acts, no ascetic though claiming to be one, not a celibate though claiming to be one, inwardly rotten, corrupt, depraved. This is called inward rottenness.”