Heart failure - as nemi describes - can be a chronic condition. You can have a relatively mild degree of heart failure for years, and it will make you a bit breathless and tired, but won't necessarily kill you. A heart attack is an acute event - again, as nemi accurately says - usually involving loss of circulation to a portion of the heart muscle. The amount of muscle that dies will determine whether the pump fails completely, and you die, or whether it carries on a bit less efficiently than before, but still keeping you alive.