In one embodiment, associated differential processing of decapsulated packets is performed using Service Function Instances (SFIs) identified by Service Function Values (SFVs) derived from their encapsulating transport packets. By using different SFVs associated with different processing policies within a same processing context, one embodiment performs differential processing of streams of packets (arriving in transport packets) as identified by the particular SFV obtained from each particular transport packet. In other words, the processing policy identifies processing performed on the corresponding decapsulated original packet, not processing of the transport packet. Thus, if the original packet is an Internet Protocol (IP) packet, the SFI identifies Layer 3 processing that is performed on the original IP packet. Additionally, one embodiment uses a route advertising protocol (e.g., Border Gateway Protocol) to distribute associations between different SFVs and different addresses in a processing context (e.g., VRF).