A lot of folks are confused about the differences here.
Azure Storage
Essential storage services in the cloud. Provides a core set of non-relational storage and processing abstractions at massive scale. Azure is built from the ground up for the cloud.
Sql Services
Rich database services in the cloud.
Extends the power of sql server in a scalable way to the cloud. SQL Services is based on a SQL Server foundation. It adds to the standard platform a lot of innovation in scale, HA, lights out operation, etc.