Sql-server – Compatibility level when upgrading a SQL Server 2005 database to SQL Server 2012

Compatibility level simply changes the language syntax that is supported by the SQL Statements. This will cause all the execution plans to be expired and force them to be recompiled. It has nothing to do with the data storage engine or the way that the data is written to the disk.

Once a database is attached to a SQL 2012 instance, it is in the SQL 2012 storage format and can't be moved back to an older version of SQL (no matter what setting the compatibility level is set to).

The link provided by @Shark (http://msdn.microsoft.com/en-us/library/bb510680%28v=sql.110%29.aspx) in the comments provides some additional reading on the subject.

Turning my comments to answer :

SSMS is just a tool to connect to SQL Server.

You did an inplace upgrade, but were connecting to SQL Server 2012 using SSMS 2008R2 and SSMS 2012.

Using T-SQL - will give you the correct version:

SELECT
   SERVERPROPERTY ('MachineName') AS PhysicalMachineName,
   SERVERPROPERTY ('ServerName') AS SQLServerName,
   SERVERPROPERTY ('Edition') AS ServerEdition,
   CAST(SUBSTRING(@@Version,charindex('SQL',@@version, 1),15) AS VARCHAR(255)) +  ' + ' 
       + CAST (SERVERPROPERTY ('productlevel')AS VARCHAR (50)) + ' + (Build'
       + CAST (SERVERPROPERTY ('ProductVersion') AS VARCHAR (50)) +')' AS ProductVersion,
    RIGHT(@@version, (Len(@@Version)-charindex('Windows',@@version, 1))+1) AS [O.S.],
 SERVERPROPERTY ('Collation') AS Collation

Best practice:

• Before upgrade - run the above script to get the version and after upgrade, run it to make sure that you are on correct right version.
• Always use the latest version of SSMS (regardless of SQL Server version).