The 'new' page shows the latest questions asthey get posted, regardless of the topic of the question. The 'topics' page shows the questions in that topic, so if no-one posts a question about maths, for example, then there won't be maths questions on the 'new' page, but there will be loads of maths questions if you go to the maths topic page. There might also be some differences because some questions are uncategorised and won't show up on the topic pages.
On the main topic page when you haven't selected a particular topic, it comes up with different stuff to the new page because if they were the same what would be the point of having both? Im not sure how they sort the topics page - maybe they just mix it up randomly?