This is probably too general a question to ask without some specific context, but I'm going to give it a shot anyway:

**What are the practical differences between using a Lorentzian function and using a Gaussian function for the purposes of fitting?**

They obviously both have different mathematical formulas, but to my (untrained) eye they both seem to model similar curves, perhaps even curves that could be reached exactly by either function given the right inputs.

If we're talking about fitting (which we are...), then presumably the person choosing between one or the other is interested in the values of the chosen function's variables (or some other feature of the curve like its height or FWHM), once the fitting has been done. **Why?** Presumably, the function is chosen since its mathematical formula instrinsicly relates to some part of the system that produced the data, but what has the Lorentzian got that the Gaussian doesn't, or vice-versa? (Or any other curve, for that matter?)

Ok, I really do apologise - I know this is a poor (and poorly worded) question. Hopefully somebody understands what I'm trying to get at and can point me in the right direction.