can somebody please explain "trans" to me??

" It's suspected testosterone provides a sporting advantage"

Not "suspected" but absolutely certain that high levels of testosterone provide a significant advantage in sports - in endurance, strength, and recovery.

Should just clarify that intersex is a group of medical conditions where there are hormonal or chromosomal disorders. There is no robust evidence that transgender ism is in any way linked to intersex conditions.

I can't find that whole study devil so I don't know what complete overlap means. Yes I was referring to Semenya. She is probably intersex (definitely not trans) but when testosterone was limited to a lower level her performance was far worse than now the limit is raised to 10. Suggesting that higher levels potentially confer an advantage and therefore trans women are likely to have an advantage as they could be at the top of the range.

OP Sexing the Body (Anne Fausto-Sterling) is a really interesting read about these things and what we can do for intersex children - I think the author says 1 in 100 live births are intersex

"a study of endocrine profiles in 693 elite athletes published in 2014 found that, while 13.7% of women athletes had high levels of testosterone, 16.5% of men had low levels of testosterone levels. The authors noted that there is "complete overlap between the sexes", concluding, "The IOC definition of a woman as one who has a ‘normal’ testosterone level is untenable."" from the Wikipedia entry for hyperandrogenism (which is what Caster Semenya has, I think that's the athlete you're referring to)

LEM the categories you've described are now all part of the "transgender" umbrella. And so a trans woman can denote a woman who's had years of hormone treatment and sex reassignment surgery. Or it can be someone who is a male in appearance, hasn't made any steps to alter their physiology to be more like a female (hormones or surgery) but feels that they are a woman.
The furore is about the impact this may have on females. For example, the Olympic committee are suggesting a testosterone level of under 10 and "feels like a woman" would enable a transgender woman to compete against females. The female range is something like 0.5 to 3 and even women with elevated testosterone are usually under 5. It's suspected testosterone provides a sporting advantage (hence why lots of testosterone doping went on in the past). Males also have physical differences in their pelvises, lungs and circulatory system that improve their sporting performance. So many people feel it's unfair to female competitors to compete against trans women. Some people also worry it will lead to the exclusion of females from competitive sport as they won't be able to compete with the trans competitors at the highest levels. Some of this is already being debated as the women's 800m at Rio had medallists who are known or suspected of being intersex with elevated testosterone.

There is also the concept of the cotton ceiling. Some trans women argue that because gender is more important in defining them as men or women than biology, that their penises are female and that lesbians who won't have sex because they have a penis are transphobic. Lesbians who say they don't want to have sex wuth a penis are being redefined as "vagina fetishists". Many people believe this to be hostile to lesbians and bordering on rape. Although it sounds like scare mongering and an extreme position, it is in fact the logical end point of saying a woman is defined by a feeling rather than by biology.

Recent events here were sparked by a transwoman called Ada Wells who said police officers should be murdered. Afa says lesbians who wont have sex with a penis are transphobic. They (preferred pronouns) called a female student who disagreed with them cuntscum. Some people feel that it's difficult to accept a person who can refer to females as "cuntscum" as a woman. Ada was elected LG BT officer at Edinburgh uni and so was supposed to represent lesbians alongside trans people. thetab.com/uk/edinburgh/2016/08/23/ada-wells-resigns-eusas-lgbt-officer-25017

I think This article sums up the issues quite well