>which imo is different, because people there are actively using medicine to change facts about their body, which is not necessary true for any transgender?

Transgender people can get HRT, socially transition, and undergo GCS. The people who use the term "transsexual" to describe themselves today are usually doing so to draw a line in the sand between those who are "trenders" and those who are "true trans". This line in the sand can be identifying as a man or woman and not taking anything else seriously (regardless of HRT and GCS status), demanding rigid gender role conformity, or wanting to exclude those who are unable to afford/access HRT and/or GCS from being trans. If you want to see how deep this rabbit hole goes, google "truscum" and "transmedicalism".

The term "transgender" is considered the more appropriate term, and the initial push for it was that "transsexual" sounded like it was a sexual orientation. It is only relatively recently that using "transsexual" became a bit of a political stance within the trans community.

> And what makes cis-gender then, except the fact that you are fine to be called he/she?

If you are cisgender, you agree with the sex you were assigned at birth. That does not mean you must agree with or conform to most or all of the cultural expectations foisted upon you due to what you were assigned at birth, just that the sex you were assigned at birth seems right and does not clash with your gender identity.[0]

There is some debate over whether non-binary individuals are transgender, but given that most definitions of transgender revolve around someone's gender identity being at odds with the sex they were assigned at birth, unless they were pronounced non-binary at birth (which does not happen to my knowledge), they are trans. That said, using the transgender label is an individual decision - trans people who "go stealth" (typically involving moving to a new place and abandoning your old friends so nobody would know you are trans and never telling anyone about your past) would not use the label publicly, but it does not make them not-trans. In addition, many non-binary people view themselves as unworthy of the transgender label or do not use it in order to avoid stigma and invasive questions. This is a personal choice and I do not blame people for not wanting to tell others they are trans, whether they identify firmly as male or female, or somewhere in-between.

[0] I want to elaborate on this point - gender identity can really be thought of as the "sex" of your brain. The sexual differentiation of the genitals occurs during the first 2 months of pregnancy, while the sexual differentiation of the brain occurs during the second half of pregnancy. If there are plenty of androgens (testosterone, DHT, etc) in the womb during the first 2 months but few during the second half, you could have a child with masculinized genitals but a feminized brain (a trans woman), and vice-versa for trans men.[1] (I have not found any research related to this and non-binary individuals, unfortunately.) However, an imbalance between these periods does not guarantee a trans child - we do not fully understand the mechanisms at play, but it appears that there is a genetic component,[2] so there is no way to predict if someone will turn out trans or not.

[1] https://pubmed.ncbi.nlm.nih.gov/21094885/

[2] http://www.hawaii.edu/PCSS/biblio/articles/2010to2014/2013-t...