The SQL server refers to a platform for retaining and managing data and this is usually hosed on any server within your
data center. This means you get to control hardware and networking, but you will have to sacrifice this control when you move to the cloud.
In Microsoft Azure there are multiple offerings and its data centers will look after the infrastructure and maintenance so that you do no longer have to worry about these. The key difference between SQL server in
Microsoft Azure and SQL database is mainly one of IaaS vs. PaaS.
The SQL database is essentially a high-end reliable secure database which you may employ for building data driven apps and sites and you do not have to manage the infrastructure. SQL server in Azure is multi-tenant and required to share the resources with all other users. You can compare their respective communication architecture to note the distinction between on-premise
SQL server and cloud-based Azure.
In the on-site SQL, apps can talk directly to the server across LAN using TDS protocol across IP/TCP. But in Azure, the applications will have to communicate through network firewalls and reach Azure Gateway through the Internet. While for SQL server which may communicate through a configurable port, communications with SQL has to happen through port 1433.