NORMAL refers to data that are from a normally distributed (Gaussian) distribution (whose histogram is shaped like a bell shaped curve.)

CATEGORICAL refers to nominal data such as male/female, hair colors, yes/no, or any observations that are categorized rather than measured.

INDEPENDENT refers to samples that do not contain the same persons, subjects or entities. For example, this might be two group of different people, where they groups are created by sampling from the same population, and each person chosen is randomly assigned to one of the two groups.

RELATED refers to samples where measures are taken on related entities. For example, a group of 10 people are weighted, then placed on a month diet and then weighed again. Since the two data points (before diet and after diet) were measured on the same individual, the date are related, sometimes called a repeated measure.