While these 2 entities overlap each other significantly and may be used as a replacement of other at times, there are still a few basic differences outlined below:
1. Sourcing Rules (SR) specify how an item (or group of items) are sourced for replenishment by an entity (say customer/ organization etc). Please note that its expressed in terms of receiving entity.
2. Bill of Distribution (BOD) specify how an item is supplied by an entity (say organization). This is expressed in terms of supplying entity
3. While BOD can only be assigned to internal organizations (could be CM or suppliers if modelled as an organization), Souricng Rule can be assigned to any type of entity including customers, suppliers, organizations and even regions & zones.
4. Typically usage of BOD vs. SR may be dependent on you supply chain structure. If a make organization is supplying to multiple distribution centers etc, BOD may help reduce data setup volume. Instead if a distribution center is sourcing from multiple organizations, SR may be a better choice.
5. If you're using regions & zones or customer locations to model how ATP/ ASCP selects a ship-from organization for Sales Orders, SR is only supported mechanism (unless these customers are modelled as organization)
6. For suppliers (not modelled as Org), SR is only option.