They are the same thing really. Article marketing is usually seen as a way to get incoming links whereas bum marketing is usually focused on getting quality traffic from the author link. Its a very subtle difference.
I think basically, both are same. You write article and then submit them to article directories. In return you get back links + traffic.
Article marketing is a type of bum marketing. Other types of bum marketing might be links from free blogs, free classifieds, etc.
There is no difference. To make money off of it, he just slapped a curious name on an already existing method. To me there is no term as bum marketing. It is strictly called article marketing.