BAM started as a stats page and built up a general BOINC account manager that allows you to manage multiple PCs from one point, attaching etc to various projects of which WCG is one. BAM doesn't host any projects, it merely allows you to connect your client to them and manage them from a central point.
World Community Grid started out with a single purpose application, originally developed by United Devices. It moved from there to the BOINC platform. To be clear, WCG existed BEFORE the Berkley Open Infrastructure for Network Computing (BOINC) was released. WCG host a number of sub projects, giving them server and technical resources provided by IBM to get their projects up and running. The projects are selected based on merit among other technical criteria and hosted for free.

There has been confusion in the past with people becoming quite frustrated that they couldn't connect directly to certain WCG sub-projects from their BOINC client, and even after it being explained to them they still couldn't get their head around it and left the project. The projects you see under BAM are full projects in their own right and can be connected to directly from your BOINC client. They pay for their own hosting and server resources in various ways ranging from university research grants to private funding on the part of the project organiser.

You cant manage WCG in detail under BAM AFAIK... to BAM/BOINC, WCG is a single project. You always have to go to the WCG Device manager to select sciences of choice.