If you're running SRM 4.x or earlier, your ODBC connection is a 32-bit DSN. You can view those by running %systemroot%\sysWOW64\odbcad32.exe
If you're on 5.x, then it's possible (though not recommended) that SRM is using the same ODBC DSN as vCenter, but is logging in with a different SQL user that has its default DB set to the SRM database.