Consider a tree $T$. A branch $B$ of a tree $T$ is just a proper subtree of $T$ (that is a subtree $B \subset T$ and $B \neq T$). Lets consider $B_1$ and $B_2$, two branches of a tree such that $B_1$ is not a subtree of $B_2$ and $B_2$ is not a subtree of $B_1$. Is there a terminology, a specific wording, to qualify such a relation between two branches?
The expression "disjoint" seems natural to me, but I'm not sure if it is used often and it may not be the best (for example the property is true for two branches with the same root, but those branches are connected, so "disjoint" might be a bit confusing for this special case.)