In the first year at Oxford, the Mathematics & Statistics course is identical to the Mathematics course. This means that you will have 5 exams at the end of the year. The first will be on algebra, the second on analysis, then probability and statistics, the fourth on geometry, dynamics and constructive mathematics, and the final exam will be on multivariable calculus and fourier series. These are all core modules, so must be taken. On top of this, during Hilary term (2nd term) you will also have to do a computational maths project, but this is only worth a very small proportion of your overall mark.
It is in the second year that these courses start to differ, albeit only slightly. Both courses require you to sit 3 exams, in Linear Algebra, Metric Spaces & Complex Analysis and Differential Equations, as well as a short options paper (generally students take 3 short options, but you only have to answer questions on 2 of them in the exam). Then there are the long options! (you have to do 5) For these, you get a choice of 9 different modules – at least at the minute you do! These include the likes of topology, integration, probability, statistics etc. However, in the M&S course, you have to take the probability and the statistics courses as part of your long options, so you only have 3 remaining options. There is an extra option included in Simulation and Statistical Programming, which students taking the M&S course can choose as one of their long options. Other than this, the 2nd year is exactly the same too!
The third years are where there is a bit more separation between the courses. Both courses require you to do 8 modules – in the maths course this is totally unrestricted – you can choose exactly which modules you want to do, out of the 35 or so offered! In the M&S course, you are required to take certain statistics modules, which aren’t all available for pure mathematics students to take, so you’re slightly more limited.
Both courses are certainly very similar to start with and then branch off in different directions later on in the course, and there is often the chance to switch between the two during your time at Oxford, if you feel that you’d like to. You’d need to talk to your college tutor and they’d have to allow it, however there are generally a few students who move from the mathematics course, to the maths & stats course, normally during 2nd year.
If you are unsure as to which course to apply for, remember that at least to start with the difference in the courses is very small! It might be a good idea to see how much you like the statistics courses over other modules in the first year, since this will give you an idea as to whether you’d really like to do more stats, or in fact there are other modules you prefer. But since it is generally easy to switch between the two courses in the first couple of years, if you realise you’d rather be on the other, then that can normally be sorted out!