It's usually in the scale of the project. Often a GB project will be a "local" project contained within one department, whilst a BB project will be a cross departments project. That said, it will depend from organisation to organisation, and some will use project value as a differentiator.
I think it also pertinent to remember that in some organisations, the only difference between GB and BB is that BB is a full-time role, whilst GB is part-time. This in itself may well place limitations on the type of project undertaken.
Bottom line...it depends