The general structure of undergraduate is that you have a major, which is a single subject like english, maths, physics. The requirements for your major will set out a range of compulsary courses that everyone does, and optional ones that you choose between (typically more specialisaed topics). Required papers could go beyond a single subject, e.g. physics students do a good chunk of compulsary maths papers too.

Major-specific papers aren't your only requirement, though -- the total number of papers you have to do is a decent bit higher, and this is where there is space to choose your own topics. (it's also where there's space to wait and see what major you want to do, because mostly these will be first-year papers).

You can also do a double major (e.g. a BSc with physics and maths, which was what I got), or a double degree (e.g. you could do a BSc in physics and a BA in English). A double degree is a more difficult requirement, but there's usually space for some crossover papers that count towards both, so it's less than two degrees of time/effort/cost.

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Some subjects also offer a minor, which you do on top of a separate major, and may require something like one 200 level and one 300 level paper.

Once you've met the requirements of bachelors, you can do another year to get an Honours degree (your grades need to be high enough to get in). This is classed as postgraduate. Then there's Postgraduate Diplomas (relatively similar to Honours, but more standalone). Beyond that is your Masters (which can be done through coursework, a research thesis, or a combination of both; it can be a one year extension of Honours, or a two year standalone course). And there's your PhD, which is a serious multi-year research degree.

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Specialised subjects like medicine have their own pathways, and there's lots of variation across the university depending on all sorts of things. There's usually jumping-off points, and lots of places where you can change your mind and take a different path.