The graph that represents a Deep Boltzmann Machine can be any weighted undirected graph. However, the graph that represents a Deep Belief Network must be a connection of graphs that represent Restricted Boltzmann Machines. Those graphs are biparite, so there are two groups of vertices in those graphs so that every edge connects two vertices from different groups. Those groups are usually the visible and hidden components of the machine.
Learning is hard and impractical and hard in a general Deep Boltzmann Machine, but easier and practical in a Restricted Boltzmann Machine and hence in a Deep Belief Network, which is a connection of some of these machines.