A heart attack (MI) is caused by the blockage of an artery around the heart. Heart muscle beyond the clot dies if emergency care isn't provided ASAP and can lead to CHF and/or death.
Heart Failure (CHF-Congestive Heart Failure-CHF) is weakness and inadequate pumping of the heart cuasing fluid backup to the legs (right sided heart failure) or backup of fluid into the lungs (left-sided heart failure). Heart failure can be caused by an MI but also other illnesses/disease process, and certain medications (ie some chemotherapies).