Your GCSE years (or what would have been called O-levels a long time ago) are done over two years in schools; Year 10 (aged 14-15) and Year 11 (aged 15-16). Your A-levels consist of an AS year and an A2 year; Year 12 (aged 16-17) and Year 13 (aged 17-18).
A student studying AS Mathematics only will do 3 modules; on the Edexcel exam board, these are C1, C2, and anyone from D1, S1 or M1. A student studying A-level Maths over two years does C1, C2, and anyone from D1, S1 or M1 in Year 12, and C3, C4, and another applied module. There are limitations as to which applied module combination you can do. For example, you can do M1 + M2, S1 + S2, S1 + M1, and D1 + D2, but not S1 + D2, or S2 + M2.
A student studying A-level Further Maths will do those 6 modules listed above (C1-4 + 2 applied) in Year 12, and then another 6 in Year 13 (FP1, either one of FP2 or FP3, and 4 applied units / 3 if you did FP1+FP2+FP3).
Here's a list of what's taught in each module for Edexcel in the UK.
http://www.edexcel.com/migrationdocuments/GCE New GCE/UA024850 GCE in Mathematics issue 2 180510.pdf
There is a third qualification available called Further Maths (Additional) which requires that you do all 18 modules (C1-4, FP1-3, D1-2, S1-4, M1-5).
The grading works as follows; to gain an A in Maths you need 480/600 total over the 6 modules. To gain the A*, you need 480/600 and an average of 90 in C3 and C4 combined. For Further Maths, you need 480/600 for the A, but an average of 90 across your 3 best modules for the A*.
At the beginning of Year 13, you apply to universities with your AS grades, and sometimes they ask you for an interview and possibly give you an offer, usually based on 3 A-levels. This might be A*AA; this means you must achieve that at the end of Year 13. Sometimes they do ask for 4, and 5 is extremely rare. Some people who have done A-levels already by the end of Year 12 might just get a single grade offer of "A*" in the remaining A-level they have to do. If you're doing Maths at a top university, they require that you take STEP. These are three 3-hour-long papers (STEP I, II, III) each marked out of 120. They are graded on a scale of S, 1, 2, 3, and U, where S is the highest grade. Typically a top university (e.g. Cambridge) will give you an offer of A*AA and 1,1 in STEP. The worst offer I have seen is somebody have A*A*A* + S,1 in STEP, but that was a rare occurrence. STEP is not to be underestimated; I have seen students get all A* at GCSE and A-level but end up with a 3,3 in STEP. It's easily one of the hardest maths papers you'll ever sit in your life if you've never done any olympiad stuff.