Hello @Bjorn ten Hoeve
I believe they are just two different log on names, so you can go with it.
AD domain short name is referred as the NetBIOS Name (as in the AD logon name <DOMAIN>\<username>).
Domain\User is the "old" logon format, called down-level logon name. Also known by the names SAMAccountName and pre-Windows 2000 logon name
The slashed format (DOMAIN\username) is actually the NetBIOS equivalent of the domain's DNS name (domain.company.local).
Active Directory: Best Practices for Internal Domain and Network Names
Understanding Active Directory Naming Formats
Hope this helps!
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Best Regards
Karlie