Believe
G4100
πιστεύω
pisteuō
pist-yoo'-o
From G4102; to have faith (in, upon, or with respect to, a person or thing), that is, credit; by implication to entrust (especially ones spiritual well being to Christ): - believe (-r), commit (to trust), put in trust with.
Faith
G4102
πίστις
pistis
pis'-tis
From G3982; persuasion, that is, credence; moral conviction (of religious truth, or the truthfulness of God or a religious teacher), especially reliance upon Christ for salvation; abstractly constancy in such profession; by extension the system of religious (Gospel) truth itself: - assurance, belief, believe, faith, fidelity.
Trust
G1679
ἐλπίζω
elpizō
el-pid'-zo
From G1680; to expect or confide: - (have, thing) hope (-d) (for), trust.
Notice that believe and faith are intermingled Read them carefully you wil see they are.
Hm trust means to expect. I expect that God will live up to his word and not lie about healing.
Jer 17:14 Heal me, O LORD, and I shall be healed; save me, and I shall be saved: for thou art my praise.
Healing
H7495
רפה רפא
râphâ' râphâh
raw-faw', raw-faw'
A primitive root; properly to mend (by stitching), that is, (figuratively) to cure: - cure, (cause to) heal, physician, repair, X thoroughly, make whole. See H7503.
Isn't he wonderful that he loves us enough to heal us.