Oud, Aoud, oudh, aloeswood, agar, and agarwood are all the same thing.
Agar is the Indian word for the tree itself, or the fragrant heartwood of the tree, that produces the resin. It is derived from the ancient Sanskrit word aguru.
Agarwood is the most common English term for it, and aloeswood is sometimes used as well (although I have seen it used more in write-ups of products of the Japanese incense tradition).
Oud (عود) is an arabic word that literally means wood, however in perfumery/incense the term is used to refer to the same thing as above, i.e. agar/agarwood.
I think the reason why the term Oud/Aoud is more popular in the west, more so than agarwood or aloeswood, is because Pierre Montale played a large role in bringing this rare fragrant wood to the attention of the western market. And he used the Arabic term (and not the one more popular in Indian or Japanese traditions) for reasons obvious to anyone who knows the story behind the Montale oud line. Whether that 'oud' is real or synthetic is of course a different topic. : )