Whats business economics? Is that a major at UNSW? Economics is so broad so I'll just summarise the 3 economics majors @ UNSW.
The financial economics major at UNSW is concerned with forecast modelling, by looking at past data. E.g. given the time series for GDP of last 30 years, fit a model to it, try to forecast the future GDP.
The econometrics major is about building models to explain results. E.g. you have a set of HSC results from a class, you take everyone's details like age, family income, race, etc. and you build a model to try explain the HSC results, such as how race affect HSC results. There's some forecasting involved too, like once you have a model, given a set of data on family income, race, etc., what do we think his HSC mark will be.
The economics major is a bit more general, I don't know too much about it but its more to do with economic theory and policies I think.