Different uni will have different focus, but generally the differences are like this:

"Finance" is geared towards understanding financial operations from a business point of view. It is less technical than financial mathematics, but it gives you a broad picture of the financial sector as a whole. You will be exposed to materials like financial management, capital markets and investment strategies, corporate financial decisions etc

"Financial Mathematics" is essentially Applied Mathematics in the field of finance, so you will be studying a lot of mathematics. It is more technical, since it's mostly Mathematics. You will be starting with basic mathematics courses: calculus, differential equations, probability, statistics, and then move on to applying those in finance (such as studying about asset pricing).

In terms of career prospect, I believe they are both equally wide.

This post has been edited by Seiryu: Mar 11 2012, 11:09 AM