The categories of sex were originally established to divide members of a set of conspecifics into subsets that can join genetic material with each other in sexual reproduction. This simple description omits mention of individuals that have been neutered, members that are too immature to function reproductively, members that are too old to function reproductively, etc. The original article says that the categories of sex "refer to complementary groups that combine genetic material in order to reproduce."
This diagram show how one set of things in the universe, a set formed by conspecific mammals, can be further divided into those who are at least potentially able to produce ova, those among them that actually do produce ova, those that originally were at least potentially capable of producing ova or sperm but who have been neutered, etc. There is an overlap of the two main sub-sets because a small number of individuals can produce both sperm and ova.
The diagram is actually oversimplified because some individuals are incapable of ever producing viable ova or sperm because of factors such as chromosome abnormalities that produce limitations that may not be easily determined.
On the basis of the above understanding of mammalian sexuality, a simple picture of physiological sex was developed according to which animals are divided into immature, mature, over-aged, and neutered males and females. In addition, a very small minority of individuals were noted that seemed to possess characteristics of both sexes, e.g., an individual might have both a penis and a vagina. Humans have a tendency to dichotomize things in their experience, and the presence of "non-complying" individuals has been the source of much discomfiture in some quarters. Part of the problem with the understanding created on this level has been that individuals who appear to be of one sex may not have the actual reproductive capabilities of that sex. For instance, a human male whose body was not virilized in the expected way during gestation may grow up looking and behaving in all ways like a woman, yet that individual will be incapable of producing ova and giving birth to a child.
While the two charts seem to discuss the same phenomena from different points of view, special attention should be paid to the fact that the center parts, the part that diagrams overlapping sets, will not necessarily be the same.
Historically, the next development was the discovery of chromosomal sex. The simple understanding was that XX individuals are females and XY individuals are males. That discovery seemed to confirm and explain the commonsense idea that humans and many other animals divided neatly into males and females. Before long, that simplistic understanding was confounded by new discoveries. One of these discoveries was that XX and XY were not the only chromosomal possibilities. The original article says, "In mammals, birds, and many other species (sic), sex is determined by the sex chromosomes, called X and Y in mammals, and Z and W in birds. Males typically have one of each (XY), while females typically have two X chromosomes (XX)." This formulation neatly sidesteps the instances in which there is only a single X chromosome present, or in which there are more than two sex chromosomes present.
