I'm not having a go at you..but is that not taught in the EMT course? Golly.
An infarction is localised cell death caused by an occlusion of the blood supply to that area. It can be caused by a number of things and happen in many places throughout the body, though some are more prone than others. Its most infamous manifestation is the Acute Myocardial Infarction.
Angina pectoris is descriptive of a set of symptoms (central, retrosternal pain, tightness, SOB ) that form a syndrome, not a particular disease process and it can be caused by a number of things, most common of which is narrowing or the arteries because of atherosclerotic plaque.
The typical AMI has it's origins early in life. Some have even suggested that plaque begins to form on the artery's walls in the womb, but it any case, it starts young. The details of its birth and formation you can read for yourself in any good pathophys textbook, but in short a plaque is a thrombogenic lipid rich interior encased in a more robust collagen cap. As plaques expand into the lumen of the artery, they take up space where blood is supposed to be flowing. This happens concurrently, all over the body, but the heart and brain are the most susceptible to reduced blood flow. The narrowing means that the heart gets less blood, which means less O2 (at the same time because of the narrowing/hardening or arteries, it has to use more O2, to work harder to get blood around the body, so its a double whammy). Often a person in the later stages of this disease may experience pain on exertion, which then dissipates when they rest. This is because while exercising, the heart needs more O2...O2 which it cannot get, so it 'screams' in pain/tightness/discomfort. But when the person rests, so can the heart and so it requires less O2. Now that the heart is less demanding, the O2 supply its getting through the narrowed arteries is just enough again, so the pain goes away. This is stable angina, or angina pectoris.
Now in a case where one of these plaques burst and the thrombogenic interior is exposed to the blood stream, it does just that...it generates thrombi, which block the supply of blood. There are a number of ways in which this happen, but in a general sense, the vast majority of infarcts are caused by complete (or near enough) blockages like this. It is relatively sudden and complete, so the areas that can't get O2, failing some fine diagnosis and expeditious treatment, will die. This is an AMI.
The world is never so simple though; UA/nSTEMIs can provide a world of confusion to you if you are simply trying to break things down to angina and infarct, but that can come later.
With any chest pain, you should be asking the pt (amongst other things) about when the pain came on, what they were doing when it did and if anything made the pain better/was it constant.
The picture of angina is typically someone who experiences chest pain and excessive SOB while they were doing exercise, but when they sat down it went away. Angina is also more responsive to treatments like nitro and O2. It also tends not last for two long. Some say 5 mins, some say 10, the AHA says a maximum of 20; but put it this way, if a person has had the same crushing chest pain for an hour now....its not stable angina/angina pectoris.
Unstable angina and MIs on the other hand can come on at rest (although they can come on anytime) and tend not to improve when they sit down and take a breather. They tend not to be as responsive to treatment, sometimes not at all. The pain remains in intensity or may get worse. Often pt will have a history of angina that has been getting worse lately; this is a big warning sign and one of the criteria for upgrading a diagnosis of stable angina/angina pectoris, to unstable angina, which, if you are only having two buckets, goes in the 'heart attack' bucket rather than the 'plain old angina' bucket.
I'm told few people ever conform to the classic picture of a heart attack, but those rules above should do you well in general.
Some reading...
Angina Pectoris
http://www.merck.com/mmpe/sec07/ch073/ch073b.html
AMI
http://www.merck.com/mmpe/sec07/ch073/ch073c.html