Shalva gave very good definitions of the different types of breeding. There are a few concepts that you need to understand other than those things, as well.
1. Breeding is not black and white. It is more shades of gray-the longer a breeder breeds, the more shades of gray they will see. This does not make them a bad breeder, it actually makes them a good breeder because there are very few absolutes when dealing with genetics.
2. You can have an outcrossed pedigree that has a very low COI and still have it be a bad breeding decision. A breeder needs to look at the whole BIG picture. There is more to take into consideration than just a COI when breeding. A COI is simply a coefficient of inbreeding. However, in goldens, we have many very well known littermates that were brothers that stood at stud, we also have a few pairs of brother/sister combinations that were very popular-meaning the brother was used at stud quite often and the sister was an oustanding dam many times over so there were lots of puppies put in homes where they would be competing and eventually breeding. We also have some very prolific litters of dogs that are often seen in pedigrees. One such example of brothers would be Tristan(CH Asterlings Go Get'em Gangbuster) and Ace(CH Asterling's Buster Keaton). These brothers could be in a pedigree many times and it would never show up in a COI because a COI is the measure of the SAME DOG in a pedigree and not littermates or other closely related relatives.
3. Another way you can have a very low COI and still have it be a bad breeding decision is if the dogs with the low COI's have bad temperaments, have spotty health information or all died early deaths. Sorry, I would much rather have a higher COI and have health, temperament and longevity.
4. If you have dogs that have lived well into their teens, were healthy for that long life, had good temperaments and produced strong clearances as well as producing good type-you would WANT to linebreed on those dogs to maintain those things in a pedigree. A COI can be higher because one dog appears more than once in a pedigree and other than that one or two dogs, still not be a closely related pedigree because all the other dogs in the 3 or 5 generation pedigree do not repeat. Genetic influence tables are actually a better indication of these type of things and will give you a much bigger picture.
5. Goldens did not come from a very large gene pool. All goldens descend back to one pair and goldens are not an old breed like many of the breeds that are recognized by the AKC. For example, the curly coated retriever is believed to be one of the oldest retrieving breeds. So, when you have a limited gene pool and all dogs go back to a particular subset of dogs, there is going to be a certain amount of linebreeding done. Linebreeding is how the golden became a golden. Lord Tweedmouth actually kept pretty detailed breeding records and I think many would be surprised to learn how goldens actually came about.
A person is really limiting themselves when they make broad statements and won't even look at linebreeding. We are not talking about people-this is not something that is taboo. All animals do a certain amount of linebreeding. Terriers are believed to be one of the healthier groups of the dogs recognized by the AKC and they practice inbreeding(breeding father to daughter, etc) quite often.
I am not advocating very high co-efficients of inbreeding. There must be some genetic diversity to maintain a breed, however, there must also be a certain amount of linebreeding to keep the breed as it is(the way it looks, acts, etc-that is defined as type) Linebreeding is what sets the different characteristics that are type. There is just a lot more to understand about the different types of breeding than reading a couple articles on the internet.
