The BBC has not only drunk the KoolAid, it's opened up a franchise and is enthusiastically promoting. This is their helpful guide. (my bold)
Transgender
This is an umbrella term for people whose gender is different from their "assigned" sex at birth - that written on their birth certificate. Gender can refer to one's own, internal sense of being a man or woman, or another type that doesn't fit either category. Gender can also be expressed externally - through clothing, behaviour, body characteristics and so on.
Transsexual
This is a term used by some people who permanently change their bodies, usually, but not always, using hormones or surgery. But some people who go through this process - known as the "transition" - prefer to be known simply as transgender, rather than transsexual. It's best to ask which people prefer.
Non-binary
Non-binary people are those who don't feel male or female. They may feel like both or like something in between. They may have a gender that changes over time or they may not relate to gender at all.
Cisgender
This describes someone who is not transgender. For instance, someone who is named a boy at birth and continues to live as a man would be cisgender. This covers the majority of the population.
"He" or "she"?
Using the appropriate pronouns when talking to someone who is transgender works on the basis of respect for the individual. Generally the name the person chooses to use indicates their gender preference. So, a transgender person called Steve would be referred to as "he", while another called Rachel would be "she". But if you are unsure, it's best to ask the person politely how they wish to be known. This is especially so if you suspect someone identifies as non-binary, in which case a neutral term like "they" may be more appropriate.
Transgender man/transgender woman
People assigned female at birth but living as a man may describe themselves as a "transgender man", while those assigned male at birth but living as a woman may call themselves a "transgender woman". These terms can be shortened to "trans man" or "trans woman".
Some may also use the acronyms FtM (female-to-male) and MtF (male-to-female). Many prefer simply to be identified simply as a "man" or a "woman".
Cross-dresser
This describes a person who wears the clothes usually associated with the "opposite "sex. This is seen as a form of gender expression. The word "transvestite" is not used much these days. And the expression "drag queen" is different, meaning a man who dresses "as a woman" for purposes of entertainment.
'Ask. Listen. Respect'
Journalist and campaigner Jane Fae suggests it doesn't have to be complicated dealing with transgender terms. "People are individuals," she says. Ask politely, listen to what individuals have to say and respect what they tell you. It's a principle and an approach to life that will take you a long way - and not just with the transgender community."