Semantics. From wikipedia:
The UML class diagram for the Strategy
pattern is the same as the diagram for
the Bridge pattern. However, these two
design patterns aren't the same in
their intent. While the Strategy
pattern is meant for behavior, the
Bridge pattern is meant for structure.
The coupling between the context and
the strategies is tighter than the
coupling between the abstraction and
the implementation in the Bridge
pattern.
As I understand it, you're using the strategy pattern when you're abstracting behavior that could be provided from an external source (eg. config could specify to load some plugin assembly), and you're using the bridge pattern when you use the same constructs to make your code a bit neater. The actual code will look very similar - you're just applying the patterns for slightly different reasons.
HTH,
Kent