An extension to AI becomes set of AI too, so it is an AI field in the way where AI is not only Learning. AI taking into account many levels of abstraction, embodied AI and multimodal interaction is also DAI.
Distributed AI means AI solved by multiple smart or reasoning agents (communicant object, physical or software) where size of agents can be a simple rule or can be a human or more ambient or pervasive structure. Sensing, Wrapping, Communication, Orchestration, Reasoning (Fission,Fusion,Evaluation,Decision), and Acting can be made by multimodal messages (ACL, KRL, WebServices, Ontologies, OWL, RDF, WRL, W3C models) to drive hardware parts and use shared software parts. So distributed AI is very useful for Architectures of AI Systems, IOT or Sensors network, Agents in Cloud, Big Data, Ambient AI, Network, Pervasive Intelligence. In brief, DAI is what has been implemented by Google, Amazon, MS,... in their Cloud even if they tend to highlight their Deep learning tools, many AI algorithms are provided which are not Deep learning or just learning. DAI is Big AI or Deep AI.
i gave some implementation examples in my PhD thesis and book.