Parametric and non-parametric tests differ in their assumptions about the population. Parametric tests assume the population is normally distributed and have equal variances, while non-parametric tests make no assumptions. Parametric tests are more powerful but require their assumptions to be met. Non-parametric tests are simpler and not affected by outliers. The document provides examples of common parametric and non-parametric tests for different study types such as comparing two or more groups or measuring the association between variables.