My question Just Another Polyglot Hacker! was marked as a duplicate of Write a polyglot that prints the language's name. Now, our scoring rules are completely different. Why are they considered dupes?
I think it's a bit unfortunate that this question was asked in the context of two rather similar scoring systems and is now used as a reference on community consensus.
I agree with the existing answers, that a question is a duplicate if answers from an old one can be reused on the new one. However, what all of them neglect (and what I think is a very important caveat to that rule of thumb): I think for the new challenge to qualify as a duplicate, those old answers also have to be competitive.
In the example of this question both challenges were about a mixed scoring between number of languages and code length. But take for example two identical challenges, where one is code-golf and one is fastest-code. Competitive code golf answers are likely to be brute force solutions, or written in things like GolfScript, which are notoriously slow. Competitive fastest-code answers likely contain a lot of code for clever optimisations and are written in fast but more bloated languages like C(++) or Java. Hence, while answers to either challenge would be valid on the other, there's little point in using one for both of them.
So here is what I think our policy should be: when we assess whether a challenge is a duplicate of another, we should ask ourselves "Can answers from one question be copied over to the other with little or no modification and still be competitive?" In particular, most tasks should make for completely different challenges if posed as fastest code or code golf, but I'm sure there are other combinations, where a change in scoring system can make a significant difference.
The criteria I like to apply (and this is not by any means official rules) is one regarding the answers to the question:
If answers can be copy/pasted from one challenge to another (with minor modifications), then the two challenges are too similar, and the new one can no longer be considered novel enough to pose a challenge.
Like so many things on CodeGolf, it depends.
The question to ask is "Are good entries for one challenge good entries for the other?" If the answer is yes, then I would consider them to be duplicates even it the change in scoring would change the "winner".
If the Answer is not, then you clearly have a different challenge.
Sometimes the answer will be "Well, uhm, ... you see ... hmmm, maybe?", which is a hard case.
Taking advantage of the sand box would probably help you to ensure enough difference to satisfy.
To this particular pair I'd say that the possibly significant difference is in the requirement for rigorous correctness. The scoring difference is a quibble and would not qualify them as distinct to my mind (moderator hat very much off).
I 'test' for duplicates in the manner described in the other answers, that is, if two questions can be answered by the same response they are duplicates. In this case there was a distinct difference (IMO) because the requirement for the later question was only tangentially (e.g. in case of a tie) related to golfing, and was focused primarily on number of languages, whereas the other question focused on golfing more. This is not an arbitrary difference because it inherently allows for some more wordy languages to be used (e.g. Java), making answers to the new one potentially more multifarious in their language use. This is however ambiguous in the test for originality because while a response to the earlier question would a good response to the later one, the reverse is not necessarily true. In essence the answers to the first question can be considered a proper subset of the possible answers to the second. Therefore, in this case I wouldn't consider them duplicates, but I wouldn't consider the later question wholly original either.