Each of those test is suited to a particular data type. The Pearson Product-Moment is used on interval and ratio data, the Point Biserial where one variable is continuous and the other dichotomous, and the Thurstone Rank Order when the data are ordinal. That may be the case, but correlation alone cannot prove causality. See the section, Scatterplots, to see some correlations of two variables graphed. Often, the goal of statistics is not to describe but rather to predict.
Prediction is the explicit goal of inferential statistics.
Data from samples are extrapolated to populations and that extrapolation is made with a predetermined degree of statistical confidence. Samples A sample is any group selected from a population for study by a researcher. However, the power of samples differs markedly depending on the type and size of the sample chosen. Non-random samples will usually not lead to accurate prediction. However, random samples help prediction tremendously.