Microsoft's SQL Server is a relational database management system (RDBMS) that runs as a server providing multi-user access to a number of databases. It originated from the Sybase SQL Server codebase, which is why both products use the extension of SQL called Transact-SQL (T-SQL).
Microsoft's SQL Server is a suite of relational database management system (RDBMS) products providing multi-user database access functionality. It originated from Sybase SQL Server 4.x codebase and Transact-SQL dialect (T-SQL), but forked significantly since then.
SQL Server is available in multiple versions, typically identified by release year, and versions are subdivided into editions to distinguish between product functionality.
The SQL Server product range is split broadly into 4 categories:
SQL Server main suite of enterprise and developer server products. Primary differences are licencing costs, capacities, and components included in the product, with some minor differences supported language features. Standard components include db language and storage server, developer tools, ETL tools, schedulers, replication. Other components include OLAP, reporting, parallel compute. Components runs as NT Services.
SQL Server Express free for use and distribution but reduced engine performance, functionality and capacity than found it's other server siblings. Focused on small deployments. Runs as an NT Service.
SQL Server Compact an embeddable subset of SQL Server. Like Express edition is has reduced language, functionality and capacity, but is free to distribute. It's focused on small installations and desktop applications where it's small footprint and no-management-required features are a great advantage.
SQL Azure completely managed, hosted, high-availability instance of SQL Server 2005 with some language syntax support federated query, operated in Microsoft Azure datacenters.