SQL Server 2008 SSMS accessing SQL Server 2012 instance

SQL Server management Studio's Backward and Forward compatibility.

SQL Server 2008 and SQL Server 2012 are two separate versions of databases.

Also, SSMS (SQL Server Management Studio) of SQL Server 2008 and SQL Server 2012 have different look and feel (UI).

But, SQL Server 2008 SSMS can still successfully access and connect to SQL Server 2012 instance.
Similarly, SQL Server 2012 can connect to SQL Server 2008 instance.