There is a key difference though - none of the YC questions are about the planning bit of a business plan. None of them are about what you're going to do in the near term future. It's all about what you've done so far and where you believe you could be when you exit.
The issue with business plans isn't that they include a report on what you've done to date. It's the idea that you can reasonably predict what you plan to do over the next year or two. Lots of more traditional businesses can do that, and a business plan is appropriate for them, but a YC startup needs to be significantly more agile than that. Any plan will certainly be wrong, so there no point wasting time making one.