Some of the ways in which they differ:
1) some of them (regression, back-propagation neural network) require "supervision", i.e. the training set includes both the inputs and the desired output. Others can learn in "unsupervised" mode, meaning that given a mass of different cases they can divide them into sensible categories.
2) some of them are better at dealing with non-linear relationships than others. Knowledge of the basic physics of your system of interest can suggest to you whether this is important for your purpose or not
3) some of them scale better to very large systems than others; what works best for a few thousand cases may not be able to scale to trillions of cases in an economical manner.
So, perhaps you can add details like whether you are needing supervised or unsupervised, how big the dataset is, and what kind of mathematical relationships you expect, and we could give you a better answer to this question.