ArcSDE is included in ArcGIS Desktop and ArcGIS Server. You get all the libraries and files needed to be able to connect to a DBMS database when installing ArcGIS Desktop or ArcGIS Server (the SQL Server Native Client is used). When you make a database in your DBMS a geodatabase, you create a set of special system tables (called repository) which makes it possible to implement ArcGIS behaviour and logic within DBMS database.
In order to "make" a database an enterprise geodatabase (aka SDE geodatabase), you need to have ArcGIS Server license. You can also "make" a database to become a workgroup geodatabase (aka SDE Personal) with SQL Server Express. There are some capacity limitations here as well as number of connecting users.
When you use versioning in your enterprise geodatabase, you use ArcSDE functionality that is built within the ArcGIS. It doesn't really matter how you access your geodatabase; if you use DC, then you use libraries that are included with ArcGIS (without installing explicitly ArcSDE libraries). If you would use ArcSDE Application Server connection, you would need to install ArcSDE software to let ArcGIS clients to connect to DBMS geodatabase by using an ArcSDE service.