Both Yahoo Pulsar and Apache DistributedLog are built over Apache BookKeeper. They have different focuses but also share a lot of similarities on design principles and implementation details.
Pulsar is a full fledged pub/sub messaging system that provides very flexible messaging model, while DistriubtedLog focuses more on buidling a replicated log store that offers replicated log as a storage primitive that other applications/systems can use. In theory, Pulsar can use DistributedLog to build its messaging system.