Arabian Oud is the name of a Saudi Arabia based company specializing in oud wood, incense, and oil based perfumes, many of which contain oud oil. Here are links to their websites. Bear in mind that these websites are generally ignored by the company, and that the product information is usually out of date. The UK website may be more current than the other one.http://www.arabianoud.com/en02/default.asp
(English version of Saudi site)http://www.arabianoud.co.uk/flash.php
As far as I know there is no separate type of oud known as Arabian oud. But it has traditionally been so popular in the region, which is closer to Europe than the Far East, that many people associate the use of oud with Arabia. Oud itself comes from India, Bangladesh, Burma, Thailand, Cambodia, and other places in SE Asia, including some of the island nations.
In the Arabian peninsula, ouds from India are generally the highest regarded, followed by those from Cambodia. I don't know why this is, if it is just a regional preference based on the way these ouds smell, or because they have been easiest to get. Some oils are available as unblended products from a particular region, but most companies offer their own blends of various oils as well as mukhallets, or mixtures with various other ingredients such as amber, patchouly, saffron, labdanum, etc.
Good luck in your oud investigations!