This paper reviews and discusses what is known about the relationship between identity in state, allele frequency, inbreeding coefficients, and identity by descent in various uses of these terms. Generic definitions of inbreeding coefficients are given, as ratios of differences of probabilities of identity in state. Then some of their properties are derived from an assumption in terms of differences between distributions of coalescence times of different genes. These inbreeding coefficients give an approximate measurement of how much higher the probability of recent coalescence is for some pair of genes relative to another pair. Such a measure is in general not equivalent to identity by descent; rather, it approximates a ratio of differences of probabilities of identity by descent. These results are contrasted with some other formulas relating identity, allele frequency, and inbreeding coefficients. Additional assumptions are necessary to obtain most of them, and some of these assumptions are not always correct, for example when there is localized dispersal. Therefore, definitions based on such formulas are not always well-formulated. By contrast, the generic definitions are both well-formulated and more broadly applicable.