They should report different names in some cases. See Books Online @@Servername topic:
Although the @@SERVERNAME function and the SERVERNAME property of SERVERPROPERTY function may return strings with similar formats, the information can be different. The SERVERNAME property automatically reports changes in the network name of the computer.
In contrast, @@SERVERNAME does not report such changes. @@SERVERNAME reports changes made to the local server name using the sp_addserver or sp_dropserver stored procedure..........."