The domestic dog, like the domestic cat is still very similar to the wild wolf in terms of genetics. It is true that our choices have meant that there is a huge range of domestic dog breeds.
So how has the domestic dog changed? Well the domestic dog has been bred to be easier to control, and this almost always comes with a reduction in intelligence. Having said that, wolves are incredibly intelligent, which means that even with less brains domestic dogs are capable of incredible featss of thinking.