Sorrow, grief, heartache, heartbreak, anguish, woe, regret, though not close synonyms, share the idea of distress of mind.
Sorrow is the most general term, implying a sense of loss or of guilt.
Grief denotes intense emotional suffering or poignant sorrow especially for some real and definite cause (compare GRIEVE ), but grief may also denote a more mundane distress of mind that is representative of the distress and trials of day-to-day life or often of a particular situation in life.
Heartache is used especially of persistent and deep sorrow that is slow to heal but that often gives little or no outward indication.
Heartbreak can imply a yet deeper and more crushing grief.
Anguish implies a distress of mind that is excruciating or torturing almost beyond bearing.
Woe implies a deep or inconsolable misery or distress usually induced by grief.
Regret seldom implies a sorrow that shows itself in tears or sobs or moans; usually it connotes such pain of mind as deep disappointment, fruitless longing, heartache, or spiritual anguish; consequently the term is applicable within a wide range that begins with the disappointment one feels, sometimes sincerely but sometimes merely as suggested by the language required by convention, in declining an invitation and ends with the pangs of remorse for something done or left undone or of hopeless repining for what can never be restored.