This appears to be a relatively poorly worded question (The question on the form, that is - not the question asked here!)
I checked with a friend who works for Singapore Airlines, and apparently the intent of this question is whether you have entered using a passport from a different country, or in a different name. ie, the fact that you have simply renewed your existing passport (with the same name, and issued by the same country) does not entail a "different passport".
A Google search seems to concur with this - in particular this blog post where the person reports answering "Yes" on the grounds of having renewed their previous passport, and was told that this was not the correct way to answer that question.
And finally, the fact that you are required to attach a separate piece of paper with details if you do answer "yes" to this question implies it's an uncommon answer - if everyone who had simply renewed their passport had to reply yes then you would expect them to include a space on the form itself to supply the details.
So in your case it seems fairly clear you should answer "No", presuming your old passport is from the same country, and in the same name.