Uniform differential item functioning (DIF) exists when the statistical relationship between item response and group is constant for all levels of a matching variable. Two other types of DIF are defined based on differences in item response functions (IRFs) among the groups of examinees: unidirectional DIF (the IRFs do not cross) and parallel DIF (the IRFs are the same shape but shifted from one another by a constant, i.e., the IRFs differ only in location). It is shown that these three types of DIF are not equivalent and the relationships among them are examined in this paper for two item response categories, two groups, and an ideal continuous univariate matching variable. The results imply that unidirectional and parallel DIF which have been considered uniform DIF by several authors are not uniform DIF. For example, it is shown in this paper that parallel three-parameter logistic IRFs do not result in uniform DIF. It is suggested that the term “uniform DIF” be reserved for the condition in which the association between the item response and group is constant for all values of the matching variable, as distinguished from parallel and unidirectional DIF.