I would say that the terminology is pretty good in this space, and BDWGC is a conservative tracing GC. A tracing GC determines reachability by following (i.e. tracing) chains of references. A precise GC will retain exactly the set of reachable objects, a conservative GC will retain potentially more.

Tracing GCs might be precise (or not), they might handle internal-pointers (or not), they might move the data (or not), they might handle variable sized allocations (or not).