The simple breakdown to make it a little easier to understand (and sadly, the WHO article breaks this guideline). For this, since we're in the MTF section, I'm going to use MTF examples where necessary (Sorry guys!):
Sex: Male/Female
Gender: Masculine/Feminine or "Man" / "Woman"
Transgender: Broadly speaking anyone whose gender identity(internal sense of self), gender expression(how one outwardly presents themselves), and biological sex are not or have not always been aligned. Cisgender, therefore is someone whose sex and gender are and have been in conventional alignment. This is the "umbrella" usage of the word transgender, since this can apply to crossdressers (gender identity masculine, gender expression feminine, biological sex male), non-transitioning transsexuals (gender identity feminine, gender expression masculine, biological sex male), transitioned transsexuals (gender identity feminine*, gender expression feminine*, biological sex female*), drag queens, androgynes, genderqueers, and so on. We could also add an axis for sex identity that would be the biological analogue of gender identity, but this isn't a commonly referenced idea.
*Formerly masculine or male
Transsexual: Someone who has taken steps, or would if possible take steps to alter their biological sex. (Notice, this does not specify which steps.)
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Now, when it comes to sex, this is where it gets a little trickier since the usefulness of distinguishing male from female depends upon what is being discussed. There's basically no hard line you can draw where someone won't end up on the wrong side of it, whether due to intersex conditions, genital reconstruction, accident or misfortune damaging reproductive organs, hormone imbalances, and so on.
Chromosomes: This is a common one since it determines, in large part, who is capable of producing viable gametes, and on paper determines physical characteristics. However, I shouldn't have to explain the difference between genotype and phenotype. What actually develops for an individual is influenced by many other factors. Also, it's disingenuous to declare this to be the sole determinant if a person has not themselves had a karyotype analysis done to determine if they are in fact who they claim to be. So this one is out. c.f. Klinefelter Syndrome
Genitals and gonads: Technically separate, but they are similar enough for our purposes. Sex organ development is largely influenced by prenatal and postnatal hormones, not chromosomes. An imbalance in utero can lead to ambiguous genitalia. Sometimes this can be ambiguous enough that doctors and parents are basically taking a 50/50 shot that they guessed right for their child's identity in the future. In the worst cases, surgery is performed early on to "correct" these children before they can either consent or dispute their assigned sex. c.f. Intersex
Hormones: Simple enough. They influence nearly everything about your sex differentiated characteristics, from mood to physical development. This is a wide spectrum with typical females producing significantly higher quantities of estrogens and males producing significantly higher qualities of androgens. But people are known to have widely varying levels even for their identified sex. c.f. Complete Androgen Insensitivity Syndrome, Polycystic Ovary Syndrome
Secondary Sex Characteristics: These are largely influenced by hormones, but they play a large role in how others identify a person's sex on sight. (That's the motivation for HRT for many transsexuals) However, there are cross-sex characteristics that are fairly common in the sex not typically associated with them. c.f. Hirsutism (male-type hairiness in females), Gynecomastia (female-type breast growth in males)
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So, where does one draw the line that doesn't leave some folks on the wrong side? And if you notice, none of those disorders on that list were Gender Dysphoria. Not all of them even cause infertility, either.
The easiest and simplest answer is to allow people to identify themselves. At the scope of any decent scientific study or legal/bureaucratic process, self-identification should be sufficient for what is being tracked. If it is so sensitive that this is not sufficient, then it's probably more helpful to disregard sex entirely and focus on delineating populations by the specific characteristic under review: e.g. if you want to know the influence of testosterone on hair loss, instead of studying males vs females (and simply assuming all males have higher testosterone than all females), compare high testosterone subjects to low testosterone subjects. On the other hand, if the margin of error on the assumption that all males are higher than all females is acceptable, then self-identification should suffice. Trans people aren't common enough to skew a study that badly unless trans people specifically are the topic of study.
Similarly for medicine. I now have female characteristics AND male characteristics. Whether I check M or F doesn't matter nearly as much as what organs and chemical levels I have. Those are the details the doctor actually needs. Just because the assumption that male means penis + prostate is right in most instances, what happens when a female has a prostate? Or a male has ovaries? Those are organs that can develop cancer, so knowing about their presence or absence is much more relevant than simply an M or F and assuming.
So, even when it comes to biological sex, the water is pretty muddy when you get to so-called "edge cases." And before anyone gets on any soapboxes about who is too far outside the norm to worry about, remember that everyone posting on this forum is one of those edge cases, and raising awareness and proper use of language are meant to ensure that those of us out here on the edge aren't being pushed off.