Similarity measures aim at quantifying the extent to which objects resemble each other. Many techniques in data mining, data analysis or information retrieval require a similarity measure, and selecting an appropriate measure for a given problem is a difficult task. In this paper, the diverse forms similarity measures can take are examined, as well as their relationships and respective properties. Their semantic differences are highlighted and numerical tools to quantify these differences are proposed, considering several points of view and including global and local comparisons, order-based and value-based comparisons, and mathematical properties such as derivability. The paper studies similarity measures for two types of data: binary and numerical data, i.e., set data represented by the presence or absence of characteristics and data represented by real vectors.