What is an "ordinal string comparison"? To contrast, what is a non-ordinal string comparison?
A non-ordinal string comparison may take into account other things such as iterating by actual characters and comparing them in language and culture-aware ways. This is useful for ordering things by name when showing a list to users.
It's not the same for all versions of German though. For example in Swiss German ß is not used and is replaced by "ss".
I do not know about Austrian German but I would not be surprised if they have some specificities around the letter ß.
In short: it's complicated :)