Trans people generally have gender dsyphoria, a different condition from body dysmorphia, which they usually don't have. The actual diagnostic criteria for gender dysphoria in adults and adolescents given by the DSM-5 are quite broad, and would include anyone who exhibits "A strong desire to be of […and…] be treated as a gender other than one's assigned gender" for at least six months. It also explicitly states that gender they identify as does not have to be the one opposite their birth sex. It can be neither i.e. non-binary.

By the diagnostic criteria, those non-binary students you were talking about may well have had gender dysphoria... it might have extended to discomfort with their bodies too: Did you ask any of them? Dress and presentation doesn't necessarily mean that much, especially among teenagers who are still figuring things out and might not be ready to change everything. I knew a teenage trans boy who had long, pink hair. I also knew an adult trans man with a beard who still liked to wear dresses sometimes. Being trans doesn't just mean escaping from one cage that's colored pink into another one that's colored blue.

I think it's more common for teenagers who were assigned female at birth to publicly identify as non-binary because most cis people unfortunately just perceive it as meaning "quirky tomboy," which is more socially acceptable than the transfeminine equivalent, "weird f * * ." I'm a trans woman, but I thought I was non-binary for about a year while I was in high school. I was sure as hell too scared to tell anyone that, though.

I ended up determining that I was the gender opposite the one I was assigned at birth. Some teens who identify as non-binary will probably end up identifying as their assigned gender. Others will continue to identify as non-binary: Kate Bornstein is non-binary and in their 70s. I think it's good that people get the space to explore their identity, even if a few end up having been attracted to a label for the wrong reasons.

Regarding the expanding definition of trans, in the past, trans people had to fall squarely within the norms for the gender they were transitioning to, or else they couldn't usually get treatment. For instance, Harry Benjamin, who was one of the early doctors who performed sexual reassignment surgery in the US, classified trans women into six groups, only two of which he labelled "True Transsexual" and approved for surgery. For a trans woman, you had to be attracted to men, be conventionally feminine, have believed you were a girl from an early age, etc.

Most of the trans community is glad that we've moved past this, but there's a minority that wants to bring back the stricter standards. They're called "transmedicalists" or sometimes "truscum" and and can often be identified by conspicuously using the word "transsexual" rather than "transgender" in 2020 (although some people use it for more benign reasons). They often say things like "we just think you need to have dysphoria to be trans." However, as noted, the clinical definition of gender dysphoria includes just about anyone who self-identifies as trans, and the actual argument is whether you have to be a binary gender, have meet the typical norms for that gender, and have to want to pursue all the medical options for transitioning to that gender. There's no agreed-upon word for trans people who don't meet the arbitrary standards required of a "true transsexual," but some transmedicalists call them "tucutes." Others call them "transgender" and call anyone they thing is really trans "transsexual." To be clear, though, speaking this way is very offensive to most trans people and you should never do it.