Dear Student,
Eunuch are known as the man who removes his testicles.
Transgender are the people's gender identities can be different from the sex they were assigned at birth .
Kleinfelter syndrome they have an extra X chromosome i.e a man shows characteristics of woman like gynacomastia.
Turner syndrome is the chromosomal disorder in which a female is born with only one X chromosome. It can lead to short height, failure of the ovaries to develop.
Down syndrome is the genetic disorder caused when abnormal cell division occurs that results in extra genetic material from chromosome 21.
So yes all are different conditions,some chromosomal, some mentally with different characteristics.
Regards