HEAD is different from branches in that it can point to a commit or a branch. A branch always points to a commit.

That's what I was saying.

When HEAD is in [branch] detached state, there is no branch to refer to/we can refer to. We are outside of branches.

You can still be in detached HEAD state and still be in a branch in a sense that your working tree reflects a commit that's in a series of commit that follow a certain bifurcation. If that makes any sense.

But as soon as you make changes and commit, you create a "branch within a branch" though that "branch" doesn't have a branch ref pointing to it.