Heart failure.  Two of the scariest words in the English language.   The American College of Cardiology/American Heart Association Guidelines define it as “any structural or functional cardiac disorder that impairs the ability of the ventricle to fill with or eject blood”   Simply put, any time the heart is unable to pump blood at a rate commensurate with the needs of body’s metabolizing cells, you have a case of heart failure.
Heart failure is often caused by a a defect in heart muscle contraction. In other cases, either the heart muscle itself functions properly, but the heart is faced with a load beyond its capacity; or ventricular filling is impaired.

Heart failure is only one of several possible underlying causes of the broader issue of circulatory failure in  which an abnormality of some component of circulation is responsible for inaequate cardiac output.  Circulatory failure can arise from heart failure, or from insufficient blood volume, low concentrations of oxygenated hemoglobin in arterial blood, or other circumstance that prevent an otherwise healthy heart from adequately meeting the metabolic needs of the body.