The former. The spec just says the result will be sorted, it just happens that the current implementations use a method that results in stable positioning of items with equal sort value.

There aren't a lot of places where stability matters, where it does the programmer should hopefully know and not have relied on an undefined behaviour… The most likely impact, I think, will be in UIs where the difference won't really matter but could be quite noticeable.

Do note though that "unstable" can mean two different things. A single threaded sort will produce the same result for the same input, and many parallels sorts have this property too due to the way they coordinate the threads and collate their results, so the output order of equal items is arbitrary but not random. Some parallel sorts do order items with the same sort key more randomly though due to being sensitive to timing differences caused by uncontrolled factors (the OS's scheduler and other things it is dealing with, differing IO delays if the sort is not in-memory, different numbers of threads if comparing run results with those done on other processor architectures, …). IIRC pdqsort is the former if those two types of unstable.