Maths Msci/Mmath (Same thing) is an 'integrated masters' degree, not offered at Edinburgh. 4 year course in England, 5 years in Scotland. Described elsewhere as an 'enhanced' undergraduate degree. Basically instead of doing your 3 year BSc plus Masters. You'd have to look around for opinion on which route is better though.
The Pure Math MA is what it says. Basically exactly the same as the BSc except that applied maths modules are not compulsory (eg in first year BSc students do all 6 modules, MA students don't have to do Diff. Equations or Linear Programming).