It's definitely a database. The modeling principles are different, and you won't get some of the niceties you get with a RDBMS, but it still allows for flexible querying and more.
S3 is not a database, but DynamoDB is :).
What differentiates DDB and S3 the most is cost and performance.
They're both highly-durable primitive data structures in the cloud, with a few extra features attached.
For example consistency is not "roughly the same" with DynamoDB supporting strongly consistent and atomic operations, and atomic update operations.
I was one of the top users by volume of both products when I worked at AWS.