Cure, heal, remedy mean to rectify an unhealthy or undesirable condition especially by some specific treatment (as medication).
Cure and heal may apply interchangeably to both wounds and diseases.
Often, however, they tend to be differentiated in such applications, cure more frequently implying restoration to health after disease, heal implying restoration to soundness of an affected part after a wound or lesion.
In extended use a similar distinction often holds, with cure applicable when a condition (as a state of mind or a habit of behavior) is under discussion and heal when a specific incident or event is involved; thus, one would seek to cure (not heal) mistrust but to heal (rather than cure) a breach between friends.
Remedy (see also REMEDY n) applies to the using of whatever will correct or relieve an abnormal condition (as of body or mind) whether affecting physical or mental health or causing mere local or occasional discomfort.
In extended use (see also CORRECT vb 1) remedy is often used in reference to evil conditions corrected, relieved, or counteracted by any means.