For understanding the readout for the “fit all” for the distributions, JMP gives you a few different numbers to look at.
Overall what is happening is JMP is fitting models to your data, and seeing how well they fit. This general method is Maximum Likelihood – and the -2LogLikelihood Score is the raw score of this fit. It is the long equation that is being “maximized”, and returns a score for how well your data fit each model. The larger the number, the better the fit. Not all models are the same though. Some models have only 2 parameters, others have 3 parameters (or more). Additional parameters will change how well the model fits, and it is good to have a different score that takes the number of parameters into account. This is what the AIC, which is the corrected Akaike's Information Criterion. This adjusts for the number of parameters in your model. The larger the AIC, the better the fit.
Do consider when looking at the different fits if the model is right for the data and your situation. For example, the “threshold” models move the intercept off 0, which could be dangerous (in the case of reliability), or just not make sense (for example the physics involved, etc.). Don’t forget to use your common sense!
Also, you can right click on the table in the report and sort by any column.