Cardiac Arrest - The heart stops pumping blood around the body, and the person dies. Essentially the heart goes into a massively irrregular ryhthym or stops completely, this means that the patient is not able to pump blood around thus not allowing oxygen and fuel to reach other parts of the body. Usually the course of treatment for an arrest is CPR, Defib, adreniline, oxygen, load em up and go like stink to the nearest resus room!
Mycardial Infarction - Also commonly called a heart attack. This is when one of the coronary arteries (the small blood vessels that supply oxygen and fuel to the heart muscle) becomes blocked. This causes the muscle to infarct (die!) thus preventing the heart from operating properly, leading to Cardiac Arrest. Treatemnt for an MI is oxygen, ECG, asprin, GTN, and run like a crazy man to the nearest Cardiac Care Unit or Cath Lab, and get the patient treated with an Angio.
Both are scary things and I've seen both a few times now. This is why any chest pain call will be treated with all haste, and we will send somebody out as soon as possible.