Upgrading to SQL Server 2012 from SQL Server 2008
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).