The short answer, there really are none, if you are looking at electronic implementations of them. Their physical implementations differ insofar as card indexes (Kartei, Karteikasten, etc.) use card stock, whereas slip boxes or Zettelkästen) employ lees durable paper. Luhmann, one of the people who used paper, chose it because it took up much less space than card stock and was much cheaper--especially since he used the backs of letters, bills, etc. cut in half to DinA 5 size for his Zettelkasten.
All that is irrelevant to an electronic version of card indexes. What is more relevant is how these applications categorize their contents. It could be alphabetical, numerical, a combination of the two, or systematic. Anyone of these will work, though, as most of the readers of my blog will know, I think the best way to implement such an electronic version is by dispensing with all such organization and use a hypertextual approach. But, however, that may be, there is nothing magical about "Zettelkasten." It just means slip box, no more, no less.
There are some applications that are not well designed to implement slip boxes (or whatever you want to call them), and those are applications that emulate notebooks (like Circus Ponies Notebook or OneNote, for instance). The note-book metaphor seems to go against the very nature of a slipbox. I cannot imagine how you could easily navigate the different notes once you reach 10,000 or more. This is one of the reason why notebooks of ledgers were abandoned in favor of card catalogs in libraries, for instance. And this is why the metaphor of a card box (database) is superior to that of a notebook when you need to deal with huge amounts of data. (My imagination may, however be just too limited to see how organization by notebooks might be superior, though I do not think so.)
1. Added later: Since these might also be based on databases, they may be quite capable at performing searches, but the way "stuff" is organised gets in the way (at least for me).