I didn't realise the Times wrote humorous columns!
Cross dresser: anybody who wears clothing traditionally associated with the opposite gender.
Transvestite: anybody who presents as the opposite gender (usually female), but has a core identity of their birth assigned gender.
Transgender: anybody who was born in one gender, but is actually the opposite gender.
Transsexual: (Medical) a transgender person on the transsexual care pathway.
Trans: An umbrella term for any of the above, as a shortcut for thinking about where they are.
Trams: A method of vehicular transport, and a common misspelling of trans.
Cis is a Greek word. As is Trans. Trans means "across" (so transport is literally 'carry across'), cis is 'same', so cisgender, 'same as birth assigned gender'.
(So to answer your question: the Greeks come up with these three letter things.)
P.S. There's loads of other places on the trans spectrum with labels. Bigender, gender queer, gender fluid, transmasculine, transfeminine, to name just a few.