What is Azure Cosmos DB?
A fully-managed, globally distributed NoSQL database service.

What is Azure DocumentDB?
A Azure DocumentDB is a fully managed NoSQL database service,
built for fast and predictable performance, high availability, elastic scaling,
global distribution, and ease of development.

Azure Cosmos DB can be classified as a tool in the "NoSQL Database as a Service" category,
while Hadoop is grouped under "Databases".