edit, tl;dr: What usually is meant by two planes being orthogonal to one another in geometry is their normals being orthogonal to each other.
In other words: two one-dimensional subspaces being orthogonal to each other.
2 planes have their normals being orthogonal to each others are sometimes said to be orthogonal. There it is a specific geometric orthogonality pointing out that the normals of the planes are orthogonal to each other. When talking about subspaces orthogonal to each other what is usually meant is all their vectors are pairwise orthogonal. But you can verify for yourself that 2 2D subspaces can not have 0 vector intersection in $\mathbb R^3$.
But if you think about it closer, you will see that the geometric meaning of normals being orthogonal to each other actually means the complement of set 1 and the complement of set 2 are orthogonal to each other. So there is a connection to the same orthogonality concept, but the subspaces are 1 dimensional.