As nouns the difference between emblem and sigh
is that
emblem is emblem while
sigh is a deep and prolonged audible inspiration or respiration of air, as when fatigued, frustrated, grieved, or relieved; the act of sighing.
As a verb sigh is
to inhale a larger quantity of air than usual, and immediately expel it; to make a deep single audible respiration, especially as the result or involuntary expression of fatigue, exhaustion, grief, sorrow, frustration, or the like.
As an interjection sigh is
an expression of fatigue, exhaustion, grief, sorrow, frustration, or the like, often used in casual written contexts.