Identify the type of a SQL Server backup
Restore Headeronly From Disk = '...'


There's only one SQL Server backup format. If this doesn't return anything useful then it's not a SQL Server backup file and may be something else (I can only imagine what; perhaps you'd have to open it in a text editor and see what the first few characters are). 

It will return a BackupType column:

1 = Database 
2 = Transaction log 
4 = File 
5 = Differential database 
6 = Differential file
7 = Partial 
8 = Differential partial


That would help you determine the order in which you need to restore (usually database with norecovery, then differential database with norecovery, then transaction log, then with recovery).

There are other methods to identify the file using PowerShell and SMO but this is the quickest.