The foundational distinction between emunah and bitachon is that emunah is the necessary but not sufficient ground for bitachon: Orchot Tzadikim (9:61) states plainly that the two are partners and that without emunah there can be no bitachon, while Kad HaKemach (Trust:1) elaborates that every one who trusts (bote'ach) necessarily believes (ma'amin), yet the converse does not hold — a believer may fail to trust, fearing that sin has forfeited his claim on Providence or that past miracles have already exhausted his portion of Divine favor.
Emunah, on its own terms, is the act of anchoring oneself to a fixed and reliable point: רש"ר הירש, שמות ד לא reads the root אמ"ן as denoting that stable point on which one leans and by which one is guided — an "omen," a nurse or trainer — while Gevurot Hashem (9:28) adds that emunah carries two distinct excellences: it manifests the strength and firmness of the believer's grip on reality, and it constitutes a form of adhesion (devekut) to God Himself inasmuch as it is received from Him.
Bitachon, by contrast, is the active, volitional surrender of one's affairs to Divine choice: רבינו בחיי, כד הקמח, בטחון teaches that a person must hand over all his concerns to the Divine will without any admixture of doubt, on the grounds that God who formed him in the womb knows his benefit and harm better than he does himself, so that even adversity is to be understood as loving reproof drawing him closer to the Almighty.
The Sefat Emet gives the relationship a sequential structure: Sefat Emet, Shemot, Terumah 1 reads the verse "trust in God and do good" together with the Zohar to teach that the core of bitachon is confidence in Divine assistance for the service of God, and that emunah — the recognition that all vitality flows from God — must precede it, because it is in proportion to the clarification of emunah in the heart that Divine inner life is in fact revealed.
מכתב מאליהו, חלק ה עמוד עה cites the Maharal's formulation that genuine bitachon means relying on God completely for what one needs rather than on one's own reasoning, with the understanding that God will bring one's intention into actuality — and that this applies specifically where the matter at hand is connected to the service of God.
מכתב מאליהו, חלק ה עמוד עמוד שמט sharpens the inner condition required for true bitachon, distinguishing between one who trusts merely because he hopes for a desired outcome — which is not genuine trust — and one who overcomes his own inclination and trusts because of his emunah in God, who will not abandon His servant engaged in His commandments; it is this latter trust that is itself a mitzvah, and by it the hoped-for outcome is merited.
Emunah also possesses two levels according to Rabbeinu Bahya, Devarim 13:7: the emunah of tradition received from one's ancestors, which is genuine but incomplete because it lacks the backing of wisdom and leaves a person vulnerable to heretical arguments, and the emunah grounded in knowledge and wisdom, which alone constitutes perfected faith.
מהר"י יעבץ, תהלים לג א similarly identifies two kinds of emunah — the emunah of a student and the emunah of a master — distinguishing between a belief that is implanted as a noble disposition or precious quality and fixed in the heart like nails by the intellect so that it never moves, and a more initial or dependent form of faith.
רבינו ירוחם, דעת תורה וישלח עמ' ריט illuminates the nature of emunah as an inner force rather than merely an intellectual assent: the phrase "dealing in emunah" (נשאת ונתת באמונה) means not simply "honestly" but conducting affairs with the very power by which one believes in God — a force so constitutive of the person that what he once recognized he never departs from, and which thus governs even his commercial reliability.
Rav Kook's writings develop bitachon as a quality that must be carefully guarded against distortion: Ein Aya, Shabbat 2:192 warns that bitachon, though among the holiest of character traits and a source of closeness to God and strength of soul in times of distress, must never become a cause of laziness — indeed the more deeply a person cleaves to God through bitachon, the more he should demonstrate diligence in all human activity, while Ein Aya, Berakhot 1:21 identifies bitachon as the very refuge from the entanglement of anxieties, and Ein Aya, Berakhot 9:185 describes how bitachon elevates the individual from his particular circumstances to the level of the collective, revealing the hidden good even in what appears harmful.