“Assāsa passāsa” has TWO meanings:
1. “Breathing in and out”
– That applies to “assāsa passāsā kāya saṅkhārā“, i.e., that is how the mind moves the body in the simplest way.
– That is in the “Cūḷavedalla Sutta (MN 44)“: “Assāsapassāsā kho, āvuso visākha, kāyasaṅkhāro”
2. “Assāsa” is to “take in the Noble Path” and “passāsa” is to dispel/reject the “wrong paths” with “wrong views”.
See, for example, “Assāsappatta Sutta (SN 38.5)” , “Paramassāsappatta Suttta (SN 38.6)”
Those translations are not that good.
– Basically, “Assāsappatto” is someone who has become a Sotapanna Anugami and thus has started “taking in” the Noble Path (First sutta)
– “Paramassāsappatto” is an Arahant who has completed the Path OR “completed taking in” (Second sutta)
P.S. : “patto” is “someone who got to that stage/level” AND “parama” is “ultimate”
– Assāsappatto = Assāsa + patto
– Paramassāsappatto = parama + assāsa + patto
P.P.S. Of course, it is the second meaning that pertains to Ānāpānasati meditation.