Calm, compose, quiet, quieten, still, lull, soothe, settle, tranquilize are comparable when they relate to persons and their feelings and moods and mean essentially to bring to an end or relieve from whatever distresses, agitates, or disturbs.
Calm implies a previous disordered state and denotes a returning to inner quietude especially as aided by judgment, fortitude, or faith.
Compose, often reflexive, retains its basic notion of arranging in order, specifically in an order that results in repose; it may heighten suggestions of conscious effort, resolution, and fortitude.
Quiet and quieten may connote a temporary external calmness in speech or demeanor rather than lasting inner calm.
These terms are likely to be used in indicating the effect of actions of persons in authority on others.
Still is somewhat literary or poetic and stresses the fact of cessation of agitation. It may suggest more peremptory action than the other terms compared and often connotes a return to quietude induced by power, authority, or awe.
Lull suggests the somnolence of lullaby, to which it is related.
It may, on the one hand, apply to the gentle easing of an infant into sleep (as by song or rocking) or, on the other hand, imply a sleepy relaxation into repose, complacence, unawareness, or apathy when one should be vigilant.
Soothe suggests bland, gentle mitigation, assuagement, or solace.
Settle (see also DECIDE) stresses the subsiding of swirling agitation and implies a stabilizing and easing of a mind or body previously upset (as by emotional excitement, illness, or intoxication).
Tranquilize in general use stresses the serenity and depth of peace achieved, but in recent years it has acquired a more specific though closely related medical application in which it implies a relieving of mental tension and agitation by means of medication.