What is the difference between nonbinary and transgender?
Q: Are nonbinary and transgender different things? How should these terms be used?
K: The short answer is that nonbinary (sometimes spelled non-binary) is an umbrella term that exists under the larger umbrella term, transgender. The longer answer is that it's a bit complicated. So, the term transgender is used in the Euro-American colonial gender system by people who do not identify with the gender they were assigned at birth, either part or all of the time. They might identify as a woman, a man, genderqueer, agender, genderfluid, a demiboy, etc. There's a lot of options because there's a lot of genders. People who are non-binary do not identify exclusively as men or women (but might sometimes, like if they are genderfluid they might sometimes identify with one or both binary genders, but other times might not).
So, technically, the term non-binary falls under the trans umbrella, right? If we're just talking about definitions, then by definition it would, but we are talking about people so it doesn't quite work that way. It's important to keep in mind that we are talking about people's identities. We need to respect self-identification. So, someone might be non-binary but not identify with the label transgender. And that's okay!
The way you should use these terms varies depending on the situation. The first rule is to respect self identification, so don't refer to an individual non-binary person as being transgender unless they also refer to themself that way. In the same vein, don't treat non-binary identities as being inherently separate from trans identities (for example, saying "trans and non-binary people" kind of implies that). These communities are not monoliths, so it's difficult to speak in general terms. Gender is socially constructed and personally experienced, so there's a lot of variety in how we use terms between generations, between communities, and between individuals.
S: Yes to all this. The term nonbinary can operate in two ways:
As an umbrella definition: "Nonbinary people are not exclusively male or female."
As an individual identity: "My sibling is nonbinary."
In some cases, one term may apply but not the other; for example, while I don't identify as a man or a woman and could be considered nonbinary by the first definition, I don't personally connect with the term as my specific gender identity.
An oversimplification that often works in U.S. contexts is to define "trans" as "not cisgender." This means that broadly speaking, nonbinary identities fall under the trans umbrella, because they are not cis. Again, however, individual people may or may not identify with a given term, and you need to respect whatever language someone uses for themself.
The thing to remember about all this is that both binary/nonbinary and cis/trans are false binaries that don't accurately describe a whole bunch of genders and gender systems. The very term "nonbinary" only makes sense in a society with a strong imposed gender binary, so in a culture where there isn't one of those, the word just doesn't really apply. The reason that defining "trans" as "non-cis" is an oversimplification is that there are plenty of people and groups with genders that don't use either of those concepts, and imposing the terminology is rude, inaccurate, and harmful (and usually rooted in colonialism). So while all of these terms as defined above may work fine for a lot of people, it's very important to remember that there is no inherent universal truth to them--they're just a way of describing gender in a certain social and cultural context.