I haven’t checked out Azure in a while (it was about 2 1/2 years ago since my last Azure post ), so I jumped back on to see what was different. These are more notes that I took than a complete overview on the service.
Most MSDN subscriptions include Azure credits, so if you have a subscription that’s a great way to check out the services at no risk.

Article on Azure SQL Database services vs virtual machines hosted on Azure

Azure SQL Database
DTU – Database Throughput Unit – A metric that combines I/O, CPU and memory to allow comparison between tiers.

Service Tiers – Basic, Standard, Premium – Sub-tiers within Standard and Premium
Max DB Size – Basic – 2 GB : Standard – 250 GB : Premium – 500 GB / 1 Tb
DTUs – Basic – 5 : Standard – 10-100 : Premium – 125-1750

Elastic Database Pool – Collection of databases with varying workloads that share a pool of resources. Uses eDTUs. Allows for predictable budget.

Backup:
Daily backups plus log backups every 5 minutes – Basic can go back 7 days for backups, Standard and Premium 35 days – Point in time restores also available.
Geo-Restore – Backups are stored in multiple locations, so a database can be restored in a different region if there is an issue with a particular location – All 3 tiers.
Geo-Replication – Makes a replica of a database – Standard and Active
Standard – One offline replica in a ‘paired’ region (Standard or Premium)
Active – Up to 4 secondaries – online and readable (Premium)
Manual failover

Resource Group:
When using Azure, you’ll create a Resource Group to group together items used by the same application. You’ll create a group even when only provisioning one item, this is the default container.

Limitations:
TCP/IP only – No Windows authentication
No distributed transactions

Virtual Machine:
Allows you to run other database systems (Oracle, DB2, MariaDB, etc)
Traditional SQL Server licensing
Allows DB over 1 TB- more control over configuration

Azure Products:

NoSQL:
DocumentDB: JOSN Document database
Azure Table Storage: BLOB storage – Key/Value
Hbase: Column family database – Part of HDInsight
Redis: Key/Value cache

Relational:
SQL Database: Database as a service
SQL Data Warehouse

Other:
Data Lake: Hadoop File System – Store data in its native state
Machine Learning: Cloud-base GUI
Data Factory: Cloud-based data integration
Azure Search: