【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.