§ IDefinition
The soul — for the Stoics a warm TERMpneuma pervading the body and forming with it a single living being. In the orthodox scheme the soul has eight parts: the TERMruling part plus the five senses, the faculty of speech, and the generative faculty. ψυχή is wider than TERMἡγεμονικόν: the latter is only its highest, rational part. The two words are therefore not interchangeable — where Marcus writes ψυχή he means the soul as a whole (often addressing it in the second person: ὦ ψυχή), not specifically the rational centre.
§ IISource
SVF II 826–833 (the eight-part soul); DL VII 110, 156–157; LS 53. In Marcus: Med. 2.6; 2.16; 3.16; 05-05 (many powers of the soul are in your control, not in others' praise); 05-11; 05-19 (things do not enter the soul; the soul troubles itself); 05-26 (the ruling part of the soul is unmoved by the flesh); 05-33 (guard the soul's ruling part before the body); 05-37 (a good lot — good turns of the soul, τροπαὶ ψυχῆς); 06-14 (the grades of soul — ἕξις/φύσις/ψυχή/λόγος; to value the rational-social soul); 06-29 (shameful for the soul to give way before the body); 06-32 (I am of a little body and a soul; to the body all is indifferent, to the mind what is not its activity); 06-52 (hold no opinion — the soul (ψυχή) will not be stirred up); 06-53 (get inside the soul of the speaker); 08-28 (pain does not ascend into the ψυχή unless it judges it an evil); 08-45 (no external is worth having the ψυχή become "worse than itself"); 08-51 (let the ψυχή neither contract nor burst out; it is an undefilable spring); 09-08 (μία νοερὰ ψυχή — one intelligent soul parcelled among rational beings); 11.20; the diminutive ψυχάριον ("little soul") at 04-41 (a quotation of Epictetus) and 07-16 (the ψυχάριον — that which fears, grieves, and judges); 07-66 (what ψυχή Socrates had — the one measure, not the glory).
§ IIINotes
Marcus often addresses his own soul as an interlocutor (02-06: "ὕβριζε, ὕβριζε σεαυτήν, ὦ ψυχή"; Med. 05-16; 10.1) — a rhetorical move in which the "I" detaches itself from the ψυχή in order to admonish it. When it is precisely the rational centre that forms judgments and gives assent that is meant, Marcus uses the narrower TERMἡγεμονικόν / TERMνοῦς / δαίμων; ψυχή is the general term for the animating principle.