The difference is that
Why did the developers design it that way is able to be interpreted as subjective while
Have the developers said why they designed it that way is a simple Yes/No question.
The first option is likely to be agreed as a bad question, so I will ignore it for now.
The second clearly has an answer. This answer can be definitively answered. The only problem is, if the answer is "No" how do we PROVE it?
I suggest we limit these questions even further to narrow down the vast expanse that is the internet. For an answer to be accepted, it must not only have a source, but a valid source that gamers will accept as trustworthy.
Due to that, we can narrow down "Have the developers said" to the developer's website and major news sites interviewing the developer. If it does not exist there, it is either common knowledge or not reliably known. This brings up a secondary issue:
While in the present the answer may be no, the developer may have an interview at a later time in which the reasoning is explained. This is an issue that plagues all of our answers, though. Games are updated all the time and things change. Just look at the Minecraft Update 1.6. I'm sure many of our answers have been messed up there, but this is a debate for a separate meta.
It has been raised that the question needs to stand alone, so I will refrain from mentioning answers since answering the question is apparently not part of the issue here.
The questions have already been shown as different, so why should
Have the developers said type questions be allowed. For one, if someone is asking the question, then they are looking for an answer. Whether this question comes from an issue they are facing or pure curiosity is not relevant, although issues tend to be more accepted than curiosity.
Also, these questions (which are still restricted by the other criteria) are about games, so this would be the appropriate SE for them, should it be decided to allow them.
As far as why these questions should be allowed, I ask "Why not?" It seems the purpose of this site is questions and answers, so why should we be limiting the questions you can ask?
Here are the reasons I've heard for not allowing these questions:
They are difficult to answer
I disagree. Yes/No questions are fairly simple to answer. We do these types of questions all the time. The only difference is that instead of looking at the game's wiki or a forum, answers will have to come from the developers (either game bonus content, developer website, or interview). I'd also like to point out that the help page states:
The answer to your question may not always be the one you wanted, but
that doesn’t mean it is wrong. A conclusive answer isn’t always
possible. When in doubt, ask people to cite their sources, or to
explain how/where they learned something. Even if we don’t agree with
you, or tell you exactly what you wanted to hear, remember: we’re just
trying to help.
They invite speculation and opinions
This is a problem with the answers more than the question. If I ask a question about the ending of a game that can also invite speculation, but we accept many of those types of questions. As far as the question goes,
Have the developers said makes the speculation disappear. If I use that, I have specifically stated in the question that I am not interested in opinion, I want to know about what the developer has said, if anything.
It's hard to prove an answer of "No"
If I can state that the developer's website (or game's website), major news outlets, and the game itself do not mention why, then that is sufficient proof. If a source is found other than those, it is likely unreliable and would fall under speculation.
It's not about playing games.
These questions are often times about some of the core concepts in the games we play. The Portal example mentioned is even answered in developer commentary inside the game (if I remember correctly). For example, if I asked "Has Bungie ever mentioned why they made Halo an FPS?` it is most definitely about the game. It may be partially about the game development, but it is mostly about the game.
There is no problem to be solved
Sometimes questions are asked out of curiosity rather then problems. For example, if I ask
What changes in TF2 when using Pyrovision Goggles?, there is no issue to be solved. I am simply curious as to what happens. The same thing can happen on other SE sites.
Additionally, some of these "Did the developers say..." questions could really just be about special content. For example, if you pre-order the
super-mega-ultra-delux version by spending $1,376,845.73 (USD) on Kickstarter, then you get the game, every piece of concept art for it, all the notes and documents relating to the game, a trip to the International Space Station with the developers, and a ticket good for one handshake with every world leader. I only got the base game, but I am curious about what the super-mega-ultra-delux version has in it and if it explains anything that didn't make it into the game. Perhaps even if the developers had a reason for it not making the final cut.
In this example, I am asking about content that is not in the game, but is available to those that have a special edition of the game. Say I found a Minecraft concept art online of a female character and wonder if
the developers ever mentioned why they did not include female models in the game. The answer could very well be
No, that is just a concept art piece that never made it to the final product. As of the present time, Notch has never stated why it was not included, nor has anyone at Mojang. If you want to add genders, here is a link to a mod: *link*. Of course the answer could also be,
Notch has mentioned why Minecraft was built without gender. You can read his statement [here](http://notch.tumblr.com/post/28188312756/gender-in-minecraft).
Both answers are equally valid. The question is valid, despite not being about a real issue in the game. I'm sure it is even interesting to more then just the OP. Another Minecraft related example of this would be all the Herobrine questions.
Alternatively, you can get bad questions like
Has Notch ever said why there are cows in Minecraft. We also get poorly worded questions in (other places)[Call of Duty Modern Warfare 3, Basic PC needs that are
under accepted criteria for questions.
These types of questions can be acceptable and even interesting and highly voted. Just because many of them are bad does not mean we should have a blatant ban on any question that is not related to an actual problem. As @SevenSidedDie said in the comments below:
bad questions are downvoted, not closed, and close votes are not superdownvotes.
As far as the intent of the question, that is going to ultimately be in the perspective of the OP. However, let's assume both types have the same intent. After all, asking either question usually desires an answer of the developer states.
However, the intent of a question can be hidden if the wording is bad. The latter asks, in a definitive manner, "What has the developer said, if anything". So yes, wording makes a huge difference.
Now for the alternative. Given that we should not expect every possible scenario to be listed here, I will do my best to offer 1 case in which the meaning behind the 2 different wordings is actually different. In other words, the 2 questions must be asking different things.
Assume the first question is
Why didn't the developers implement an auto-save feature? The second question would then be
Have the developers ever mentioned why they didn't implement an auto-save feature?
Say I posted the first question and my intent was to complain about something on the internet. I know this is hard to imagine, but just stick with me. In this scenario, there really is no question to be answered. The OP wanted a discussion or people to agree with them. According to the Arqade FAQ, these kinds of questions are not allowed, so if this truly is the intent then it should be closed.
Now, is it possible for the second wording of the question to give this same intent. In other words, if the question was edited into this new wording, would it still be asking the same thing. I would have to say no. If you are specifically asking
Have the developers ever mentioned... then I think it required to be about the developer's reasoning. You are not allowing interpretation nor opinion. You are asking about something specific. I do not see how asking such a question with this wording could be about basic internet complaining.
Therefore, yes the wording makes a difference. Not just in a manner of there being different words, but the 2 questions are actually asking different things.
Yes, there is a difference.
Have the developers said removes the possibility of opinion. Question wants the DEVELOPER'S WORD and ONLY the developer's word.