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.

different la ... not sure if you can get a job in m'sia with financial maths ....

That would depend on the institute itself,
financial math must not be mistaken as mathematics of finance.
I know they sound like the same thing, but it actually dont mean the same.
Each school schedule sylabus differently.

For example, my Uni take financial math as a technical subject, dealing with lots and lots of calculation of annuities,
all sorts of financial cash flows, interest rate immunisations and stuff.
Whereas Mathematics of finance (also known to be called, "mathematical finance"), is applying understanding of pure math into finance, starting rigiourously from analysis and hence probability, how to define measures on finance, proving of intuitive formulas, and the rather abstract approach to learning finance & its underlying mechanism. Which prepares you for research in related areas.

Finance is too wide, and general in context, again check with your institute bout whats covered in the course you are applying to. You dont need very high level math to do financial math (in general). but for mathematical finance (yes, thats pure math).

Dont mix up all the difference. But please, check with your school, because it is possible some school mix up the title.

where do you plan to get your degree? in the us a financial math grad would qualify for pretty much any entry level finance role.