Yeah, I called them bushes because what we bought it perhaps 2-3 ft high, with many many stems and leaves.
My partner's mom bought hazelnuts a few years ago, but hers had a single trunk each, with perhaps two branches, and they were about 5-6 ft tall.
I think they can be shaped in either direction.
Also, my partner took a Natural Resources class in college, and he remembered having to participate in a tree count in the forest. The rule was, if the trunk split below your height, then it was two trees. However, if the trunk divided into multiple directions above your height, it was a single tree. So it's all subjective, I guess!