SQL Server : differential backup not updating
The extension of a backup file is just to have a notation and easy identification. The script you are using is for Log backup and not for Differential backup.

Differential backup backs up the extents that had changes since the last full backup. Below is the t-sql for that :

BACKUP DATABASE AdventureWorks TO DISK = 'C:\AdventureWorks.DIF' WITH DIFFERENTIAL
GO


The backup that you are taking is log backup and in addition to letting you restore the backed-up transactions, a log backup truncates the log to remove the backed up log records from the log file. This is very important to have a point in time recovery and has to be scheduled to run frequently.

Please go through below link to understand how backups work :

https://technet.microsoft.com/en-us/library/2009.07.sqlbackup.aspx