Most nonbinary people consider themselves transgender, as we fall under the definition of "identifying as a gender different to the one we were assigned at birth." However, there are some nonbinary folks who object to being grouped under the trans label for a number of reasons- for instance, some intersex people who ID as nonbinary would not be trans, someone who was raised in a culture that accepts nonbinary genders and who wasn't assigned a gender at birth wouldn't be trans, some people don't identify strongly with the trans label because our experiences often differ quite a lot from our binary counterparts, some don't identify with it because binary trans communities can be quite exclusionary towards people like us unfortunately, and some people who choose not to medically transition don't feel welcome to use the identity. Those are just a few of the examples I've heard, and a lot of it tends to be backlash against the umbrella term "LGBT" which a lot of people find very restricting, as it lumps people together and excludes certain groups- a lot of nonbinary people don't like being lumped under the T, just like pansexuals/polysexuals don't like being lumped under the B, and people whose letter is often excluded (i.e. intersex people, people who just label themselves as "queer," or people who ID as ace or aro) don't like that their letter isn't included at all.

So while most nonbinary people consider themselves trans (like me!), there are some who don't. I hope that answers your question!